Question

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

Given:

A figure.

To find:

The values of x and y.

Solution:

We know that, in a right angled triangle,

$\sin \theta =\dfrac{Perpendicular}{Hypotenuse}$

$\sin 60^\circ =\dfrac{x}{16}$

$\dfrac{\sqrt{3}}{2} =\dfrac{x}{16}$

Multiply both sides by 16.

$\dfrac{\sqrt{3}}{2}\times 16=\dfrac{x}{16}\times 16$

$8\sqrt{3}=x$

And,

$\cos \theta =\dfrac{Base}{Hypotenuse}$

$\cos 60^\circ =\dfrac{y}{16}$

$\dfrac{1}{2}=\dfrac{y}{16}$

Multiply both sides by 16.

$\dfrac{16}{2}=y$

$8=y$

Therefore, the missing side lengths are $x=8\sqrt{3}$ and $y=8$.