Question

Please show work and thank youuu

Answer 1

Answer:

x = 8√2

Step-by-step explanation:

As the opposing side of the angle and the hypotenuse are given, take the sine ratio of the angle.

• sin 45° = x/16
• 1/√2 = x/16
• x = 16 / √2
• x = 16√2 / 2
• x = 8√2

Answer 2

Answer:

$\sf x=8{\sqrt{2}$

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)

Therefore, to find x we need to use the sine trig ratio.

Given:

• $\theta$ = 45°
• O = x
• H = 16

Substitute these values into the formula and solve for x:

$\implies \sf \sin(\theta)=\dfrac{O}{H}$

$\implies \sf \sin(45^{\circ})=\dfrac{x}{16}$

$\implies \sf x=16 \sin(45^{\circ})$

$\implies \sf x=16 \cdot \dfrac{\sqrt{2}}{2}$

$\implies \sf x=8{\sqrt{2}$