Questions: Find theta in degrees.

Solution Steps

The given triangle is a right triangle with sides 3, 4, and 5. The side opposite the right angle is the hypotenuse (5), and the other two sides are the legs (3 and 4).

To find the angle θ, we can use the trigonometric ratios. Specifically, we can use the tangent function, which is the ratio of the opposite side to the adjacent side.

The tangent of θ is given by: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4} \]

To find θ, we take the inverse tangent (arctan) of \(\frac{3}{4}\): \[ \theta = \arctan\left(\frac{3}{4}\right) \]

Final Answer