Applications Of Trigonometry Answers

• Applications Of Trigonometry Answers Paper
• Applications Of Trigonometry Answers 2
• Applications Of Trigonometry Answers Answer

Grade 10 trigonometry problems and questions with answers and solutions are presented.

Thus here we have discussed Trigonometry and its importance as every student of math is expected to know about the application of this branch of mathematics in daily life. Solve sample questions with answers and cross-check your answers with the NCERT Solutions on some applications of Trigonometry. Applications of Trigonometry What can you do with trig? Historically, it was developed for astronomy and geography, but scientists have been using it for centuries for other purposes, too. Besides other fields of mathematics, trig is used in physics, engineering, and chemistry.

Applications Of Trigonometry Answers Paper

Problems

1. Find x and H in the right triangle below.
   

   
   

2. Find the lengths of all sides of the right triangle below if its area is 400.
   
   
3. BH is perpendicular to AC. Find x the length of BC.
   
   
4. ABC is a right triangle with a right angle at A. Find x the length of DC.
   
   
5. In the figure below AB and CD are perpendicular to BC and the size of angle ACB is 31°. Find the length of segment BD.
   
   
6. The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle.
   
7. In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
   
8. In a right triangle ABC with angle A equal to 90°, find angle B and C so that sin(B) = cos(B).
   
9. A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect.
   
10. The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59°. Find the length of side AC.
    
11. From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building.
    
12. Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30°. The balloon rises 50 meters. Now the angle of depression to the car is 35 degrees. How far is the car from point P?
    
13. If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70° to 60°, what is the height of the building?

Solutions to the Above Problems

1. x = 10 / tan(51°) = 8.1 (2 significant digits)
   H = 10 / sin(51°) = 13 (2 significant digits)
   
2. Area = (1/2)(2x)(x) = 400
   Solve for x: x = 20 , 2x = 40
   Pythagora's theorem: (2x)² + (x)² = H²
   H = x √(5) = 20 √(5)
   
3. BH perpendicular to AC means that triangles ABH and HBC are right triangles. Hence
   tan(39°) = 11 / AH or AH = 11 / tan(39°)
   HC = 19 - AH = 19 - 11 / tan(39°)
   Pythagora's theorem applied to right triangle HBC: 11² + HC² = x²
   solve for x and substitute HC: x = √ [ 11² + (19 - 11 / tan(39°))² ]
   = 12.3 (rounded to 3 significant digits)
   
4. Since angle A is right, both triangles ABC and ABD are right and therefore we can apply Pythagora's theorem.
   14² = 10² + AD² , 16² = 10² + AC²
   Also x = AC - AD
   = √( 16² - 10² ) - √( 14² - 10² ) = 2.69 (rounded to 3 significant digits)
   
5. Use right triangle ABC to write: tan(31°) = 6 / BC , solve: BC = 6 / tan(31°)
   Use Pythagora's theorem in the right triangle BCD to write:
   9² + BC² = BD²
   Solve above for BD and substitute BC: BD = √ [ 9 + ( 6 / tan(31°) )² ]
   = 13.4 (rounded to 3 significant digits)
   
6. The triangle is right and the size one of its angles is 45°; the third angle has a size 45° and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse.
   Area = (1/2)x² = 50 , solve for x: x = 10
   We now use Pythagora to find H: x² + x² = H²
   Solve for H: H = 10 √(2)
   
7. Let a be the length of the side opposite angle A, b the length of the side adjacent to angle A and h be the length of the hypotenuse.
   tan(A) = opposite side / adjacent side = a/b = 3/4
   We can say that: a = 3k and b = 4k , where k is a coefficient of proportionality. Let us find h.
   Pythagora's theorem: h² = (3k)² + (5k)²
   Solve for h: h = 5k
   sin(A) = a / h = 3k / 5k = 3/5 and cos(A) = 4k / 5k = 4/5
   
8. Let b be the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse.
   sin(B) = b/h and cos(B) = c/h
   sin(B) = cos(B) means b/h = c/h which gives c = b
   The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of 45°.
   
9. The diagram below shows the rectangle with the diagonals and half one of the angles with size x.
   tan(x) = 5/2.5 = 2 , x = arctan(2)
   larger angle made by diagonals 2x = 2 arctan(2) = 127° (3 significant digits)
   Smaller angle made by diagonals 180 - 2x = 53°.
   
10. Let x be the length of side AC. Use the cosine law
    12² = 8² + x² - 2 · 8 · x · cos(59°)
    Solve the quadratic equation for x: x = 14.0 and x = - 5.7
    x cannot be negative and therefore the solution is x = 14.0 (rounded to one decimal place).
    
11. The diagram below show the two buildings and the angles of depression and elevation.
    tan(20°) = 200 / L
    L = 200 / tan(20°)
    tan(10°) = H2 / L
    H2 = L × tan(10°)
    = 200 × tan(10°) / tan(20°)
    Height of second building = 200 + 200 × tan(10°) / tan(20°)

More References and links on Trigonometry

Trigonometry.
Solve Trigonometry Problems.
Free Trigonometry Questions with Answers.
High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers
Middle School Maths (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
Primary Maths (Grades 4 and 5) with Free Questions and Problems With Answers
Home Page

To name a few, the practical applications are:

1. Acoustics

2. Architecture

3. Astronomy ( and Navigation)

Applications Of Trigonometry Answers 2

4. Cartography

5. Chemistry

6. Civil Engineering

7. Computer Graphics

8. Crystallography

• Applications Of Trigonometry Answers Paper
• Applications Of Trigonometry Answers 2
• Applications Of Trigonometry Answers Answer

Grade 10 trigonometry problems and questions with answers and solutions are presented.

Thus here we have discussed Trigonometry and its importance as every student of math is expected to know about the application of this branch of mathematics in daily life. Solve sample questions with answers and cross-check your answers with the NCERT Solutions on some applications of Trigonometry. Applications of Trigonometry What can you do with trig? Historically, it was developed for astronomy and geography, but scientists have been using it for centuries for other purposes, too. Besides other fields of mathematics, trig is used in physics, engineering, and chemistry.

Applications Of Trigonometry Answers Paper

Problems

1. Find x and H in the right triangle below.
   

   
   

2. Find the lengths of all sides of the right triangle below if its area is 400.
   
   
3. BH is perpendicular to AC. Find x the length of BC.
   
   
4. ABC is a right triangle with a right angle at A. Find x the length of DC.
   
   
5. In the figure below AB and CD are perpendicular to BC and the size of angle ACB is 31°. Find the length of segment BD.
   
   
6. The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle.
   
7. In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
   
8. In a right triangle ABC with angle A equal to 90°, find angle B and C so that sin(B) = cos(B).
   
9. A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect.
   
10. The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59°. Find the length of side AC.
    
11. From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building.
    
12. Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30°. The balloon rises 50 meters. Now the angle of depression to the car is 35 degrees. How far is the car from point P?
    
13. If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70° to 60°, what is the height of the building?

Solutions to the Above Problems

1. x = 10 / tan(51°) = 8.1 (2 significant digits)
   H = 10 / sin(51°) = 13 (2 significant digits)
   
2. Area = (1/2)(2x)(x) = 400
   Solve for x: x = 20 , 2x = 40
   Pythagora's theorem: (2x)² + (x)² = H²
   H = x √(5) = 20 √(5)
   
3. BH perpendicular to AC means that triangles ABH and HBC are right triangles. Hence
   tan(39°) = 11 / AH or AH = 11 / tan(39°)
   HC = 19 - AH = 19 - 11 / tan(39°)
   Pythagora's theorem applied to right triangle HBC: 11² + HC² = x²
   solve for x and substitute HC: x = √ [ 11² + (19 - 11 / tan(39°))² ]
   = 12.3 (rounded to 3 significant digits)
   
4. Since angle A is right, both triangles ABC and ABD are right and therefore we can apply Pythagora's theorem.
   14² = 10² + AD² , 16² = 10² + AC²
   Also x = AC - AD
   = √( 16² - 10² ) - √( 14² - 10² ) = 2.69 (rounded to 3 significant digits)
   
5. Use right triangle ABC to write: tan(31°) = 6 / BC , solve: BC = 6 / tan(31°)
   Use Pythagora's theorem in the right triangle BCD to write:
   9² + BC² = BD²
   Solve above for BD and substitute BC: BD = √ [ 9 + ( 6 / tan(31°) )² ]
   = 13.4 (rounded to 3 significant digits)
   
6. The triangle is right and the size one of its angles is 45°; the third angle has a size 45° and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse.
   Area = (1/2)x² = 50 , solve for x: x = 10
   We now use Pythagora to find H: x² + x² = H²
   Solve for H: H = 10 √(2)
   
7. Let a be the length of the side opposite angle A, b the length of the side adjacent to angle A and h be the length of the hypotenuse.
   tan(A) = opposite side / adjacent side = a/b = 3/4
   We can say that: a = 3k and b = 4k , where k is a coefficient of proportionality. Let us find h.
   Pythagora's theorem: h² = (3k)² + (5k)²
   Solve for h: h = 5k
   sin(A) = a / h = 3k / 5k = 3/5 and cos(A) = 4k / 5k = 4/5
   
8. Let b be the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse.
   sin(B) = b/h and cos(B) = c/h
   sin(B) = cos(B) means b/h = c/h which gives c = b
   The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of 45°.
   
9. The diagram below shows the rectangle with the diagonals and half one of the angles with size x.
   tan(x) = 5/2.5 = 2 , x = arctan(2)
   larger angle made by diagonals 2x = 2 arctan(2) = 127° (3 significant digits)
   Smaller angle made by diagonals 180 - 2x = 53°.
   
10. Let x be the length of side AC. Use the cosine law
    12² = 8² + x² - 2 · 8 · x · cos(59°)
    Solve the quadratic equation for x: x = 14.0 and x = - 5.7
    x cannot be negative and therefore the solution is x = 14.0 (rounded to one decimal place).
    
11. The diagram below show the two buildings and the angles of depression and elevation.
    tan(20°) = 200 / L
    L = 200 / tan(20°)
    tan(10°) = H2 / L
    H2 = L × tan(10°)
    = 200 × tan(10°) / tan(20°)
    Height of second building = 200 + 200 × tan(10°) / tan(20°)

More References and links on Trigonometry

Trigonometry.
Solve Trigonometry Problems.
Free Trigonometry Questions with Answers.
High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers
Middle School Maths (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
Primary Maths (Grades 4 and 5) with Free Questions and Problems With Answers
Home Page

To name a few, the practical applications are:

1. Acoustics

2. Architecture

3. Astronomy ( and Navigation)

Applications Of Trigonometry Answers 2

4. Cartography

5. Chemistry

6. Civil Engineering

7. Computer Graphics

8. Crystallography

9. Geophysics

10. Economics (Analysis of Financial Markets)

11. medical imagining

12. Seismology

13. Phonetics

14. Probability and Statistics. and etc.

What has the author C E Goodson written?

C. E. Goodson has written: 'Technical algebra with applications' -- subject(s): Algebra 'Technical trigonometry with applications' -- subject(s): Trigonometry

What has the author Newcomb Greenleaf written?

Newcomb Greenleaf has written: 'Calculator-based trigonometry with applications' -- subject(s): Calculators, Trigonometry

What are the practical applications of physics in everyday life?

An automobile is a practical application of physics in every day life. Walking and using a skateboard are also practical applications of physics.

What are the practical applications of environmental geology?

There are many practical applications of environmental geology. Some applications include studying changes in the Earth's surface and managing natural hazards.

What are the applications for francium?

No practical applications. Francium is used only for scientific studies.

Why did greek science emphasize theory over practical applications?

It is easier to theorize than it is to develop practical applications for theories. It took a long time, historically, before there was enough real scientific knowledge that scientists could easily produce practical applications for their theories.

Applications Of Trigonometry Answers Answer

What are the practical applications of electric field?

An electrical field has many applications, ex. In circuitry, power production, magnets, automobiles, etc. There are many practical applications of an electrical field, it also depends on what you are planning to do.

What has the author James E Hall written?

James E. Hall has written: 'Trigonometry; circular functions and their applications' -- subject(s): Plane trigonometry, Trigonometrical functions

What practical applications for business and technology do you foresee in our society?

There many practical applications for business and technology in the future. It is likely you will see many things become smaller and faster.