Question

Use special right triangles to solve for the exact value of y.

A. 4 square root 3

B. 8 square root 3

C. 12 square root 3

Answer 1

The answer is B 8 square root 3

Answer 2

we know that

`sin(60\°)=(√(3))/(2)`-----> equation A

`cos(60\°)=(1)/(2)` ------> equation B

In the right triangle of the figure

`sin(60\°)=(y)/(x)` -----> equate to the equation A

`(y)/(x)=(√(3))/(2)` -----> equation C

`cos(60\°)=(8)/(x)` ------> equate to the equation B

`(8)/(x)=(1)/(2)\\\\x=16`

Substitute the value of x in the equation C

`(y)/(16)=(√(3))/(2)\\ \\y=16 √(3)/2 \\ \\y=8 √(3)\ units`

therefore

the answer is the option B

8 square root 3