Question

Find the value of the variables in the image above

Answer 1

Answer:

x = 8$\sqrt{3}$ , y = 8

Step-by-step explanation:

Using the sine and cosine ratios in the right triangle and the exact values

sin60° = $\frac{\sqrt{3} }{2}$ , cos60° = $\frac{1}{2}$

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{16}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 16$\sqrt{3}$ ( divide both sides by 2 )

x = 8$\sqrt{3}$

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cos60° = $\frac{adjacent}{hypotenuse}$ = $\frac{y}{16}$ = $\frac{1}{2}$ ( cross- multiply )

2y = 16 ( divide both sides by 2 )

y = 8