Question

Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2

Answer 1

Answer:

B

Step-by-step explanation:

using the tangent ratio on the triangle on the right and the exact value

tan60° = $\sqrt{3}$ , then letting the altitude be h

tan60° = $\frac{opposite}{adjacent}$ = $\frac{11\sqrt{6} }{h}$  = $\sqrt{3}$ ( multiply both sides by h )

11$\sqrt{6}$ = h × $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

11$\sqrt{2}$ = h

using the sine ratio in the triangle on the left and the exact value

sin45° = $\frac{\sqrt{2} }{2}$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{h}{x}$ = $\frac{11\sqrt{2} }{x}$ = $\frac{\sqrt{2} }{2}$ ( cross- multiply )

$\sqrt{2}$ × x = 22$\sqrt{2}$ ( divide both sides by $\sqrt{2}$ )

x = 22