Question

solve for x.
diagram: right triangle with right angle at top right, hypotenuse (12 cm) from top left to bottom right, angle 62° at bottom right, vertical leg (x) from top right to bottom right
x = ? cm
round to the nearest hundredth.

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the hypotenuse (12 cm) and we need to find the adjacent side to the \(62^\circ\) angle (which is \(x\)). The cosine function relates the adjacent side and the hypotenuse: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\).
So, \(\cos(62^\circ)=\frac{x}{12}\).

Step2: Solve for \(x\)

Multiply both sides by 12 to isolate \(x\): \(x = 12\times\cos(62^\circ)\).
Calculate \(\cos(62^\circ)\approx0.4695\), then \(x = 12\times0.4695 = 5.634\).
Round to the nearest hundredth: \(x\approx5.63\).

Answer:

\(5.63\)