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

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.

  • 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

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 𝑚𝐴𝐶𝐵 and 𝑚𝐵𝐴𝐶, in degrees, to two decimal places.

  • A𝑚𝐴𝐶𝐵=53.13, 𝑚𝐵𝐴𝐶=36.87
  • B𝑚𝐴𝐶𝐵=38.66, 𝑚𝐵𝐴𝐶=51.34
  • C𝑚𝐴𝐶𝐵=51.34, 𝑚𝐵𝐴𝐶=38.66
  • D𝑚𝐴𝐶𝐵=36.87, 𝑚𝐵𝐴𝐶=53.13
  • E𝑚𝐴𝐶𝐵=37.99, 𝑚𝐵𝐴𝐶=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, 𝑚𝐴=43, 𝑚𝐶=47
  • B𝐴𝐵=15cm, 𝑚𝐴=34, 𝑚𝐶=56
  • C𝐴𝐵=15cm, 𝑚𝐴=35, 𝑚𝐶=55
  • D𝐴𝐵=15cm, 𝑚𝐴=42, 𝑚𝐶=48

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

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.