Lesson Worksheet: Right Triangle Trigonometry: Solving for an Angle Mathematics • 11th Grade

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In this worksheet, we will practice finding a missing angle in a right triangle using the appropriate inverse trigonometric function given two side lengths.

Q1:

The height of a ski slope is 16 metres and the length is 20 metres. Find the measure of ∠𝜃 giving the answer to two decimal places.

Q2:

For the given figure, find the measure of ∠𝐵𝐴𝐶, in degrees, to two decimal places.

Q3:

In the given figure, find the measure of angle 𝜃, in degrees, to two decimal places.

Q4:

For the given figure, find the measures of ∠𝐴𝐵𝐶 and ∠𝐴𝐶𝐵, in degrees, to two decimal places.

  • A𝑚∠𝐴𝐵𝐶=66.03∘, 𝑚∠𝐴𝐶𝐵=23.96∘
  • B𝑚∠𝐴𝐵𝐶=63.61∘, 𝑚∠𝐴𝐶𝐵=26.39∘
  • C𝑚∠𝐴𝐵𝐶=26.39∘, 𝑚∠𝐴𝐶𝐵=63.61∘
  • D𝑚∠𝐴𝐵𝐶=26.57∘, 𝑚∠𝐴𝐶𝐵=63.43∘
  • E𝑚∠𝐴𝐵𝐶=63.43∘, 𝑚∠𝐴𝐶𝐵=26.57∘

Q5:

Find the values of 𝛼 and 𝛽 giving the answer to the nearest second.

  • A𝛼=4614′18′′∘, 𝛽=3550′16′′∘
  • B𝛼=3550′16′′∘, 𝛽=4614′18′′∘
  • C𝛼=4345′42′′∘, 𝛽=4614′18′′∘
  • D𝛼=4614′18′′∘, 𝛽=4345′42′′∘

Q6:

Given the following figure, find the measures of angles ∠𝐴𝐶𝐵 and ∠𝐵𝐴𝐶 and the length of 𝐴𝐶. Give your answers to two decimal places.

  • A𝑚∠𝐴𝐶𝐵=41.63∘, 𝑚∠𝐵𝐴𝐶=48.37∘, 𝐴𝐶=9.43
  • B𝑚∠𝐴𝐶𝐵=41.63∘, 𝑚∠𝐵𝐴𝐶=48.37∘, 𝐴𝐶=12.04
  • C𝑚∠𝐴𝐶𝐵=48.37∘, 𝑚∠𝐵𝐴𝐶=41.63∘, 𝐴𝐶=9.43
  • D𝑚∠𝐴𝐶𝐵=48.37∘, 𝑚∠𝐵𝐴𝐶=41.63∘, 𝐴𝐶=11.22
  • E𝑚∠𝐴𝐶𝐵=62.73∘, 𝑚∠𝐵𝐴𝐶=27.27∘, 𝐴𝐶=10.63

Q7:

𝑋𝑌𝑍 is a right-angled triangle at 𝑌, where 𝑋𝑌=16.5cm, 𝑌𝑍=28cm, and 𝑋𝑍=32.5cm. Find the measure of ∠𝑍 giving the answer to the nearest second.

  • A5929′23′′∘
  • B2655′0′′∘
  • C4044′46′′∘
  • D3030′37′′∘

Q8:

𝐴𝐵𝐶 is a right triangle at 𝐵, where 𝐵𝐶=10cm and 𝐴𝐶=18cm. Find the length 𝐴𝐵, giving the answer to the nearest centimeter, and the measure of angles 𝐴 and 𝐶, giving the answer to the nearest degree.

  • A𝐴𝐵=15cm, 𝑚∠𝐴=43∘, 𝑚∠𝐶=47∘
  • B𝐴𝐵=15cm, 𝑚∠𝐴=34∘, 𝑚∠𝐶=56∘
  • C𝐴𝐵=15cm, 𝑚∠𝐴=35∘, 𝑚∠𝐶=55∘
  • D𝐴𝐵=15cm, 𝑚∠𝐴=42∘, 𝑚∠𝐶=48∘

Q9:

A 5 m ladder is leaning against a vertical wall such that its base is 2 m from the wall. Work out the angle between the ladder and the floor, giving your answer to two decimal places.

  • A68.19∘
  • B23.57∘
  • C66.42∘
  • D21.80∘

Q10:

A car is going down a ramp that is 10 meters high and 71 meters long. Find the angle between the ramp and the horizontal, giving the answer to the nearest second.

  • A8154′12′′∘
  • B81′2′′∘
  • C85′48′′∘
  • D815′48′′∘
  • E6231′42′′∘

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