Questions: Find x. Round your answer to the nearest tenth of a degree.

Transcript text: Find $x$. Round your answer to the nearest tenth of a degree.

Solution

Solution Steps

Step 1: Identify the Trigonometric Function

To find the angle $ x $ in the right triangle, we can use the tangent function, which relates the opposite side to the adjacent side. Here, the opposite side is 28 and the adjacent side is 21.

Step 2: Set Up the Tangent Equation

The tangent of angle $ x $ is given by: \[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{28}{21} \]

Step 3: Calculate the Tangent Value

Calculate the value of the fraction: \[ \frac{28}{21} = \frac{4}{3} \approx 1.3333 \]

Step 4: Use the Inverse Tangent Function

To find the angle $ x $, take the inverse tangent (arctan) of 1.3333: \[ x = \tan^{-1}(1.3333) \]

Step 5: Compute the Angle

Using a calculator, compute the inverse tangent: \[ x \approx 53.1^\circ \]

Final Answer

\[ x \approx 53.1^\circ \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >