Question

Find the length of each leg.

Answer 1

Answer:

see explanation

Step-by-step explanation:

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

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

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{BC}{AC}$ = $\frac{BC}{10}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2BC = 10$\sqrt{3}$ ( divide both sides by 2 )

BC = 5$\sqrt{3}$

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cos60° = $\frac{adjacent}{hypotenuse}$ = $\frac{AB}{AC}$ = $\frac{AB}{10}$ = $\frac{1}{2}$ ( cross- multiply )

2AB = 10 ( divide both sides by 2 )

AB = 5