Worksheet: Applications of Trigonometric Ratios

In this worksheet, we will practice identifying which trigonometric ratio to use to calculate sides and angles in right triangles.

Q1:

Find the area of triangle 𝐴 𝐵 𝐶 , given that 𝐴 𝐵 = 𝐴 𝐶 , 𝐵 𝐶 = 2 0 c m , and c o s 𝐵 = 5 1 3 .

Q2:

In the given figure, , , and . Calculate the length of . Give your answer to two decimal places.

  • A6.20
  • B5.20
  • C8.00
  • D9.54
  • E10.55

Q3:

A chord is drawn in a circle whose radius is 8 cm. If the measure of its central angle is 1 0 0 , calculate the length of the chord to the nearest thousandth.

Q4:

𝐴 𝐵 𝐶 𝐷 is a rhombus where the lengths of the diagonals 𝐴 𝐶 and 𝐵 𝐷 are 14.2 cm and 23.2 cm respectively. Find 𝑚 𝐴 𝐷 𝐶 giving the answer to the nearest second.

  • A 1 0 4 3 1 1 7
  • B 7 5 2 8 4 3
  • C 3 1 2 8 1 0
  • D 6 2 5 6 2 0
  • E 3 7 4 4 2 1

Q5:

From the top of a house 15 m tall, the angles of elevation and depression of the top and the base of a building are 5 9 and 4 4 respectively. Find the height of the building giving the answer to the nearest metre.

Q6:

𝐴 𝐵 𝐶 is a triangle where 𝐴 𝐶 = 3 5 c m , 𝐵 𝐶 = 2 5 c m , and 𝑚 𝐶 = 5 4 . Point 𝐷 lies on 𝐶 𝐵 where 𝐴 𝐷 𝐵 𝐶 . Find the area of 𝐴 𝐵 𝐶 giving the answer to two decimal places.

Q7:

Find the value of t a n 𝐴 .

  • A 1 7 8
  • B 4 5
  • C 5 4
  • D 8 1 7
  • E 1 0 2 7

Q8:

𝐴 𝐵 𝐶 𝐷 is a trapezium-shaped piece of land where 𝐴 𝐷 is parallel to 𝐵 𝐶 and 𝐴 𝐵 𝐵 𝐶 . Find 𝑚 𝐶 given that 𝐴 𝐷 = 2 0 m , 𝐵 𝐶 = 3 5 m , and 𝐷 𝐶 = 2 5 m . Give the answer to the nearest second.

  • A 3 8 3 9 3 5
  • B 3 6 5 2 1 2
  • C 5 1 2 0 2 5
  • D 5 3 7 4 8

Q9:

The dimensions of a rectangular garden is 20 metres by 17 metres. Triangle 𝐴 𝐸 𝐶 represents the lawn where 𝐸 𝐶 = 9 m . Find 𝐴 𝐸 𝐵 giving the answer to the nearest second.

  • A 4 0 2 1 5 2
  • B 3 2 5 4 1 9
  • C 4 9 3 8 8
  • D 5 7 5 4 1

Q10:

Find the lengths of 𝐵 𝐶 and 𝐴 𝐶 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐴 𝐵 = 1 5 c m and t a n 𝐶 = 3 4 . Give the answers to the nearest centimetre.

  • A 𝐵 𝐶 = 1 5 c m , 𝐴 𝐶 = 2 5 c m
  • B 𝐵 𝐶 = 2 5 c m , 𝐴 𝐶 = 2 0 c m
  • C 𝐵 𝐶 = 1 5 c m , 𝐴 𝐶 = 2 0 c m
  • D 𝐵 𝐶 = 2 0 c m , 𝐴 𝐶 = 2 5 c m

Q11:

Two boys are on opposite sides of a tower. They see the top of the tower at angles of elevation 3 9 and 2 6 , respectively. If the height of the tower is 21 m, find the distance between the two boys to the nearest meter.

Q12:

In the given figure, , , and . Calculate the length of . Give your answer to two decimal places.

Q13:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 , where 𝐴 𝐵 = 2 6 c m and 𝑚 𝐶 = 6 5 8 . Find the perimeter of 𝐴 𝐵 𝐶 , giving the answer to the nearest centimeter.

Q14:

𝐴 𝐵 𝐶 is a triangle where 𝐴 𝐶 = 3 8 c m , 𝐵 𝐶 = 5 4 c m , and 𝑚 𝐶 = 4 0 . Point 𝐷 lies on 𝐶 𝐵 where 𝐴 𝐷 𝐵 𝐶 . Find the area of 𝐴 𝐵 𝐶 giving the answer to two decimal places.

Q15:

Find the area of triangle 𝐴 𝐵 𝐶 , given that 𝐴 𝐵 = 𝐴 𝐶 , 𝐵 𝐶 = 4 8 c m , and c o s 𝐵 = 4 5 .

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