Question

a right triangle with one leg labeled 29, the hypotenuse labeled 58, and the angle opposite the leg of length 29 is marked with a question mark.

Explanation:

Step1: Identify triangle type

This is a right - triangle. Let the hypotenuse be \(c = 58\) and the adjacent side to the unknown angle \(\theta\) (the angle we need to find) be \(a=29\).

Step2: Use cosine formula

The cosine of an angle \(\theta\) in a right - triangle is given by \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So \(\cos\theta=\frac{29}{58}=\frac{1}{2}\).

Step3: Find the angle

We know that if \(\cos\theta = \frac{1}{2}\), and \(\theta\in[0,\frac{\pi}{2}]\) (since it's an acute angle in a right - triangle), then \(\theta = 60^{\circ}\) (because \(\cos60^{\circ}=\frac{1}{2}\)).

Answer:

The measure of the unknown angle is \(60^{\circ}\)