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Worksheet: Applications of Trigonometric Ratios

Q1:

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

Q2:

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

Q3:

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

  • A 16.000 cm
  • B 6.128 cm
  • C 15.757 cm
  • D 12.257 cm
  • E 10.285 cm

Q4:

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

  • A
  • B
  • C
  • D
  • E

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 𝐡 𝐢 is a triangle where 𝐴 𝐢 = 3 5 c m , 𝐡 𝐢 = 2 5 c m , and π‘š ∠ 𝐢 = 5 4 ∘ . Point 𝐷 lies on 𝐢 𝐡 where 𝐴 𝐷 βŸ‚ 𝐡 𝐢 . Find the area of 𝐴 𝐡 𝐢 giving the answer to two decimal places.

Q7:

𝐴 𝐡 𝐢 is a triangle where 𝐴 𝐢 = 3 8 c m , 𝐡 𝐢 = 5 4 c m , and π‘š ∠ 𝐢 = 4 0 ∘ . Point 𝐷 lies on 𝐢 𝐡 where 𝐴 𝐷 βŸ‚ 𝐡 𝐢 . Find the area of 𝐴 𝐡 𝐢 giving the answer to two decimal places.

Q8:

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

Q9:

is a trapezoid-shaped piece of land where is parallel to and . Find given that , , and . Give the answer to the nearest second.

  • A
  • B
  • C
  • D

Q10:

The dimensions of a rectangular garden is 20 meters by 17 meters. Triangle 𝐴 𝐸 𝐢 represents the lawn where 𝐸 𝐢 = 9 m . Find the value of ∠ 𝐴 𝐸 𝐡 giving the answer to the nearest second.

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

Q11:

Find the lengths of and given is a right triangle at where and . Give the answers to the nearest centimeter.

  • A ,
  • B ,
  • C ,
  • D ,

Q12:

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.

Q13:

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

Q14:

In the given figure, 𝐴 𝐡 = 6 , 𝐴 𝐷 = 3 , and π‘š ∠ 𝐴 𝐢 𝐡 = 3 3 ∘ . Calculate the length of 𝐡 𝐢 . Give your answer to two decimal places.

Q15:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where 𝐴 𝐡 = 2 6 c m and π‘š ∠ 𝐢 = 6 5 8 β€² ∘ . Find the perimeter of 𝐴 𝐡 𝐢 giving the answer to the nearest cm.