Question

this is a 30 - 60 - 90 triangle. what is the measure of x? x = ?

Explanation:

Step1: Identify side type

The side labeled 80 is the hypotenuse (opposite right angle). The side x is adjacent to the 60° angle (since angles in triangle sum to 180°, the other acute angle is 60°: 180-90-30=60).

Step2: Use cosine function

$\cos(60^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{x}{80}$

Step3: Solve for x

$\cos(60^\circ) = 0.5$, so $x = 80 \times 0.5 = 40$

Answer:

40