Question

Student NameDateStand45-45-90 Right TrianglesFind the missing side lengths. Leave your answers as radicals in simplest form.1)y2)......Sosceles8521145°8V2 45:

Answer 1

Given:

A triangle with angles 45-45-90.

Required:

Find the missing side length.

Explanation:

We will use here trigonometric ratios as:

$\begin{gathered} Cos\text{ 45}^{\circ}=\frac{3}{x} \\ x=\frac{3}{\frac{1}{\sqrt{2}}} \\ x=3\sqrt{2} \end{gathered}$

Now,

$\begin{gathered} sin45^{\circ}=\frac{y}{3\sqrt{2}} \\ \frac{1}{\sqrt{2}}=\frac{y}{3\sqrt{2}} \\ y=3 \\ \end{gathered}$

Answer:

Hence, x and y are required lengths.