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tags:
Right Triangle Special Right Triangle Trigonometry Series

Special Right Triangles Exercise 1

Author: Rachel Carlson

The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to see the answer to the problem.

Problem: Find the missing side lengths, \(b\) and \(c,\) in the triangle.

A right triangle with a 45 degree angle and side opposite is 5, the other leg is b and hypotenuse is c

<strong>Solution:</strong> \(b=5\qquad \) \(c=5\sqrt{2}\)
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<p><strong>Solution Method:</strong> Something should stand out about this right triangle: the \(45^\circ\) angle. Since we know that the sum of a triangle&#39;s angles are \(180^\circ,\) if we have a \(90^\circ\) and a \(45^\circ\) angle, the last angle must also be \(45^\circ.\) That means we have a <strong>45-45-90</strong> triangle.</p>

<p>We know the ratios the side lengths must have to one another in a 45-45-90 triangle. Therefore, we can find \(b\) and \(c\) using the side length 5.</p>

<p>Since 5 is the length of a leg of this 45-45-90 triangle, \(x=5.\) Then the legs of a 45-45-90 triangle are a 1:1 ratio, the same. So \(b=5.\) Then the hypotenuse has length \(x\sqrt{2}\), the leg times \(\sqrt{2}\). So \(c=5\sqrt{2}.\)</p>

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