Question

Find x a) 21 √2 b)7 c)21 √2/2 d)21 √3/2

Answer 1

Answer:

C

Step-by-step explanation:

Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values

sin60° = $\frac{\sqrt{3} }{2}$ , cos45° = $\frac{1}{\sqrt{2} }$ , thus

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{opp}{7\sqrt{3} }$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2 × opp = 21 ( divide both sides by 2 )

opp = $\frac{21}{2}$

Now consider the right triangle on the right, using the cosine ratio

cos45° = $\frac{adjacent}{hypotenuse}$ = $\frac{\frac{21}{2} }{x}$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

x = $\frac{21}{2}$ × $\sqrt{2}$ = $\frac{21\sqrt{2} }{2}$ → C