Question

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

A. x=24, y=8√3
B. X=8, y=24√3
C. X=24√3, y=8
D. X=8√3, Y=24

Answer 1

Answers:
x = 24
y = 8√3
Step-by-step explanation:

1) Since, the given triangle is a right triangle, and you have both an angle and the hypotenuse length, you can use some trigonometric ratios to find the variables.

2) The variables given represent:

x: adjacent-leg to angle 30°
y: opposite length to angle 30°

3) sine ratio:

sin 30° = opposite-leg / hypotenuse = y / (16√3)

⇒ y = 16√3 sin 30° = 16√3 × (1/2) = 8√3

4) cosine ratio

cos 30° = adjacent-leg / hypotenuse = x / (16√3)

⇒ x = 16√3 cos 30° = 16√3 (√3 / 2) = 16 × 3 / 2 = 24