Master Trigonometry Applications: Solve Real-World Problems with Confidence

Question 1

When using trigonometry to find the lengths of all three sides of a triangle, which trigonometric ratios are essential to use?

Accepted Answer

Sine, Cosine, Tangent

Answer

Sine, Cosine

Answer

Tangent, Cotangent

Question 2

In a right triangle with sides of length 3, 4, and 5, what is the value of the sine of the angle opposite the side of length 3?

Accepted Answer

0.6

Answer

0.8

Answer

1.0

Answer

1.2

Question 3

A plane flies 200 miles at a bearing of 120 degrees. What is the eastward component of the plane's velocity (in miles)?

Accepted Answer

150 miles

Answer

100 miles

Answer

200 miles

Answer

250 miles

Question 4

A truss is a triangular structure used in construction. If the two equal sides of a truss are 10 meters long and the included angle is 60 degrees, what is the length of the third side?

Accepted Answer

15 meters

Answer

10 meters

Answer

20 meters

Answer

25 meters

Question 5

A ship travels 60 km along a bearing of 045 degrees. Determine the distance traveled by the ship in the northward direction.

Accepted Answer

42.4 km

Answer

30 km

Answer

60 km

Answer

0 km

Question 6

From a point 50 meters away from the base of a tower, the angle of elevation to the top of the tower is measured to be 30 degrees. Calculate the height of the tower.

Accepted Answer

25√3 meters

Answer

50 meters

Answer

50√3 meters

Answer

100 meters

Question 7

A surveyor measures the angle of elevation to the top of a building to be 25 degrees. If the surveyor is standing 120 meters from the base of the building, calculate the height of the building.

Accepted Answer

58.8 meters

Answer

120 meters

Answer

240 meters

Answer

480 meters

Question 8

Which trigonometric ratio is used to find the length of the side opposite the known angle in a right-angled triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 9

If the cosine of an angle is 0.5, calculate the sine of the same angle.

Accepted Answer

0.866

Answer

0.5

Answer

1

Answer

Cannot be determined

Question 10

Which of the following is NOT a field where trigonometry is applied?

Accepted Answer

Algebra

Answer

Surveying

Answer

Navigation

Answer

Architecture

Question 11

A ladder **12 m** long is leaning against a wall. The base of the ladder is **8 m** from the wall. How high up the wall does the ladder reach?

Accepted Answer

9.6 m

Answer

10 m

Answer

12 m

Answer

6 m

Question 12

A ship leaves port and sails **60 km** due east. It then turns and sails **80 km** on a bearing of **120°**. What is the ship's final displacement from the port?

Accepted Answer

100.6 km

Answer

140 km

Answer

50 km

Question 13

A force of 100 Newtons is applied to a block at an angle of 45 degrees above the horizontal. What is the vertical component of the force?

Accepted Answer

70.7 Newtons

Answer

100 Newtons

Answer

50 Newtons

Answer

25 Newtons

Question 14

A ship sails 80 kilometers on a bearing of 045 degrees. How far east has the ship travelled?

Accepted Answer

56.6 kilometers

Answer

80 kilometers

Answer

20 kilometers

Answer

40 kilometers

Question 15

A ladder is leaning against a wall. The base of the ladder is 4 meters from the wall and the top of the ladder is 6 meters high. What is the angle that the ladder makes with the ground?

Accepted Answer

56.3 degrees

Answer

180 degrees

Answer

78.7 degrees

Answer

33.7 degrees

Question 16

A radio telescope has a parabolic dish with a diameter of 100 meters. The receiver, located at the focus of the parabola, is 25 meters away from the vertex. What is the angle of elevation from the receiver to the edge of the dish?

Accepted Answer

14.04 degrees

Answer

7.02 degrees

Answer

28.08 degrees

Answer

30 degrees

Question 17

Two forces, 10 N and 15 N, act on an object at an angle of 60 degrees to each other. What is the magnitude of the resultant force?

Accepted Answer

21.8 N

Answer

5 N

Answer

25 N

Answer

12.5 N

Question 18

A surveyor measures the angle of elevation to the top of a building as 30 degrees. Standing 100 meters from the base of the building, what is the height of the building?

Accepted Answer

57.7 meters

Answer

100 meters

Answer

30 meters

Answer

115.5 meters

Question 19

Two buildings are 50 meters apart. The angle of depression from the top of the taller building to the top of the shorter building is 20 degrees. If the taller building is 80 meters high, what is the height of the shorter building?

Accepted Answer

68.4 meters

Answer

50 meters

Answer

80 meters

Answer

20 meters

Question 20

A triangular plot of land has sides of 100 meters, 150 meters, and 200 meters. What is the area of the plot of land?

Accepted Answer

7243.2 square meters

Answer

45000 square meters

Answer

15000 square meters

Answer

30000 square meters

Question 21

An airplane flies 200 km due north and then 300 km due east. What is the magnitude of the plane's displacement from its starting point?

Accepted Answer

360.6 km

Answer

300 km

Answer

200 km

Answer

500 km

Question 22

A radio tower is 100 meters tall. A guy wire is attached to the top of the tower and anchored to the ground 50 meters from the base of the tower. What is the angle the guy wire makes with the ground?

Accepted Answer

63.4 degrees

Answer

45 degrees

Answer

90 degrees

Answer

30 degrees