How to Find Missing Sides and Angles of a Right Triangle

How to Find Missing Sides and Angles of a Right Triangle

Learn how to find the missing sides or angles of a right triangle when one length and one angle is 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 \((θ=\frac{opposite}{hypotenuse}\). sine \(45^\circ=\frac{AC}{8}→8 ×sin 45^\circ=AC\),
now use a calculator to find sin \(45^\circ\). sin \(40^\circ=\frac{\sqrt{2}}{2}→AC \cong 0.70710\)

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

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

Solution:

sine \(θ=\frac{opposite}{hypotenuse}\). sine \(40^\circ=\frac{AC}{6}→6 ×\) sine \(40^\circ=AC\),
now use a calculator to find sine \(40^\circ\). sine \(40^\circ\cong 0.642→AC \cong 3.9\)

Exercises for Finding Missing Sides and Angles of a Right Triangle

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

Answers

  • \(\color{blue}{31.4}\)
  • \(\color{blue}{7.0}\)
  • \(\color{blue}{16.2}\)
  • \(\color{blue}{31.1}\)

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