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

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.

  • A𝑚𝐴𝐵𝐶=66.03, 𝑚𝐴𝐶𝐵=23.96
  • B𝑚𝐴𝐵𝐶=63.61, 𝑚𝐴𝐶𝐵=26.39
  • C𝑚𝐴𝐵𝐶=26.39, 𝑚𝐴𝐶𝐵=63.61
  • D𝑚𝐴𝐵𝐶=26.57, 𝑚𝐴𝐶𝐵=63.43
  • E𝑚𝐴𝐵𝐶=63.43, 𝑚𝐴𝐶𝐵=26.57

Q5:

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

  • A𝛼=461418, 𝛽=355016
  • B𝛼=355016, 𝛽=461418
  • C𝛼=434542, 𝛽=461418
  • D𝛼=461418, 𝛽=434542

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.

  • A𝑚𝐴𝐶𝐵=41.63, 𝑚𝐵𝐴𝐶=48.37, 𝐴𝐶=9.43
  • B𝑚𝐴𝐶𝐵=41.63, 𝑚𝐵𝐴𝐶=48.37, 𝐴𝐶=12.04
  • C𝑚𝐴𝐶𝐵=48.37, 𝑚𝐵𝐴𝐶=41.63, 𝐴𝐶=9.43
  • D𝑚𝐴𝐶𝐵=48.37, 𝑚𝐵𝐴𝐶=41.63, 𝐴𝐶=11.22
  • E𝑚𝐴𝐶𝐵=62.73, 𝑚𝐵𝐴𝐶=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.

  • A592923
  • B26550
  • C404446
  • D303037

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, 𝑚𝐴=43, 𝑚𝐶=47
  • B𝐴𝐵=15cm, 𝑚𝐴=34, 𝑚𝐶=56
  • C𝐴𝐵=15cm, 𝑚𝐴=35, 𝑚𝐶=55
  • D𝐴𝐵=15cm, 𝑚𝐴=42, 𝑚𝐶=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.

  • A815412
  • B812
  • C8548
  • D81548
  • E623142

Practice Means Progress

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