how to find missing angles

Learn how to find the missing sides or angles of a right triangle when one length and one angle are provided.

Step by step guide to finding missing sides and angles of a Right Triangle

By using Sine, Cosine or Tangent, we can find an unknown side in a right triangle when we have one length, and one angle (apart from the right angle).
Adjacent, Opposite and Hypotenuse, in a right triangle is shown below.
Recall the three main trigonometric functions:
SOH – CAH – TOA, sin \(θ=\frac{opposite}{hypotenuse}\), Cos \(θ=\frac{adjacent}{hypotenuse}\), tan \(⁡θ=\frac{opposite}{adjacent}\)

Missing Sides and Angles of a Right Triangle – Example 1:

Find AC in the following triangle. Round answers to the nearest tenth.

Solution:

sin \(θ=\frac{opposite}{hypotenuse}\). sin \(45^\circ=\frac{AC}{8}→8 ×sin 45^\circ=AC\),
now use a calculator to find sin \(45^\circ\). sin \(45^\circ=\frac{\sqrt{2}}{2}→\cong 0.70710\)

AC= \( 0.70710 \) × \( 8 \) \( \cong 5.7 \)

Missing Sides and Angles of a Right Triangle – Example 2:

Find AC in the following triangle. Round answers to the nearest tenth.

Solution:

sin \(θ=\frac{opposite}{hypotenuse}\). sin \(40^\circ=\frac{AC}{6}→6 ×\) sin \(40^\circ=AC\),
now use a calculator to find sin \(40^\circ\). sin \(40^\circ\cong 0.642\)

AC= \( 0.642 \) × \(6 \) \( \cong 3.9 \)

Exercises for Finding Missing Sides and Angles of a Right Triangle

Find the missing side. Round answers to the nearest tenth.

Answers

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