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 trigonometric function given two side lengths.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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.

Q7:

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

Q8:

A car is going down ramp which 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
  • B98548
  • C18548
  • D8548

Q9:

A palm tree snaps due to bad winds. The vertical trunk is 5 metres tall and the inclined part is 6 metres. Find the measure of the angle between the inclined part and the ground giving the answer to the nearest second.

  • A562634
  • B333326
  • C394820
  • D501140

Q10:

𝐴𝐵𝐶𝐷 is a rhombus whose diagonals intersect at the point 𝑀 where 𝐴𝐵=11cm and 𝐴𝑀=10cm. Find the value of 𝐵𝐴𝐷 giving the answer to the nearest second.

  • A243712
  • B902423
  • C491424
  • D652248
  • E843251

This lesson includes 27 additional questions and 203 additional question variations for subscribers.

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