Lesson Worksheet: Right Triangle Trigonometry: Solving for an Angle Mathematics

Practice

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

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

Find the measure of angle 𝜃, in degrees, to two decimal places.

Question 7

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∘

Question 8

For the given figure, find angle 𝜃, in degrees, to two decimal places.

Question 9

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

  • A𝑚∠𝐴𝐶𝐵=53.13∘, 𝑚∠𝐵𝐴𝐶=36.87∘
  • B𝑚∠𝐴𝐶𝐵=38.66∘, 𝑚∠𝐵𝐴𝐶=51.34∘
  • C𝑚∠𝐴𝐶𝐵=51.34∘, 𝑚∠𝐵𝐴𝐶=38.66∘
  • D𝑚∠𝐴𝐶𝐵=36.87∘, 𝑚∠𝐵𝐴𝐶=53.13∘
  • E𝑚∠𝐴𝐶𝐵=37.99∘, 𝑚∠𝐵𝐴𝐶=52.01∘

Question 10

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∘

This lesson includes 24 additional questions and 167 additional question variations for subscribers.

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