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Lesson: Applications of Trigonometric Ratios

Video

16:24

Sample Question Videos

Worksheet • 15 Questions • 2 Videos

Q1:

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

  • A9.54
  • B10.55
  • C5.20
  • D8.00
  • E6.20

Q2:

Find the value of t a n 𝐴 .

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

Q3:

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.

Q4:

𝐴 𝐡 𝐢 𝐷 is a trapezium-shaped piece of land where 𝐴 𝐷 is parallel to 𝐡 𝐢 and 𝐴 𝐡 βŸ‚ 𝐡 𝐢 . Find π‘š ∠ 𝐢 given that 𝐴 𝐷 = 2 0 m , 𝐡 𝐢 = 3 5 m , and 𝐷 𝐢 = 2 5 m . Give the answer to the nearest second.

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

Q5:

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 centimeter.

Q6:

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.

Q7:

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.

Q8:

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

Q9:

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.

Q10:

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.

Q11:

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

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

Q12:

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

  • A 5 7 5 β€² 4 1 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 4 0 2 1 β€² 5 2 β€² β€² ∘

Q13:

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 .

Q14:

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 .

Q15:

𝐴 𝐡 𝐢 𝐷 is a rhombus where the lengths of the diagonals 𝐴 𝐢 and 𝐡 𝐷 are 14.2 cm and 23.2 cm respectively. Find π‘š ∠ 𝐴 𝐷 𝐢 giving the answer to the nearest second.

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