Question

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

Answer 1

Answer:

see explanation

Step-by-step explanation:

To find x use the sine ratio in the right triangle and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{14\sqrt{3} }{x}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

x $\sqrt{3}$ = 28$\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

x = 28

-----------------------------------------------------------

To find y use the tangent ratio in the right triangle and the exact value

tan60° = $\sqrt{3}$ , then

tan60° = $\frac{opposite}{adjacent}$ = $\frac{14\sqrt{3} }{y}$ = $\sqrt{3}$ ( multiply both sides by y )

14$\sqrt{3}$ = y $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

y = 14