Question

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

Answer 1

Answer:

B  x = 3, y= 3

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

• $\theta$ is the angle
• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse (the side opposite the right angle)

Given:

• $\theta$ = 45°
• O = $x$
• A = $y$
• H = $3\sqrt{2}$

$\implies \sin(45^{\circ})=\dfrac{x}{3\sqrt{2}}$

$\implies x=3\sqrt{2}\sin(45^{\circ})$

$\implies x=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}$

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

$\implies x=\dfrac{3 \cdot 2}{2}=3$

$\implies \cos(45^{\circ})=\dfrac{y}{3\sqrt{2}}$

$\implies y=3\sqrt{2}\cos(45^{\circ})$

$\implies y=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}$

$\implies y=\dfrac{3\sqrt{2} \sqrt{2}}{2}$

$\implies y=\dfrac{3 \cdot 2}{2}=3$