Questions: Find theta in degrees.

Transcript text: Find theta in degrees.

Solution

Solution Steps

Step 1: Identify the Right Triangle

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).

Step 2: Use Trigonometric Ratios

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.

Step 3: Calculate the Tangent of θ

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

Step 4: Find θ Using the Inverse Tangent Function

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