Questions: Use the inverse of the tangent ratio to find the approximate measure of angle B. Round your answer to the nearest whole degree.

Transcript text: Use the inverse of the tangent ratio to find the approximate measure of angle $B$. Round your answer to the nearest whole degree.

Solution

Solution Steps

Step 1: Identify the sides of the triangle

In the given right triangle, we have:

Opposite side to angle $ B $ (BC) = 20
Adjacent side to angle $ B $ (AC) = 25

Step 2: Set up the tangent ratio

The tangent of angle $ B $ is given by the ratio of the opposite side to the adjacent side: \[ \tan(B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{25} \]

Step 3: Calculate the inverse tangent

To find angle $ B $, we use the inverse tangent (arctan) function: \[ B = \tan^{-1}\left(\frac{20}{25}\right) \]

Step 4: Compute the value

Using a calculator to find the inverse tangent: \[ B = \tan^{-1}(0.8) \approx 38.66^\circ \]

Step 5: Round to the nearest whole degree

Rounding 38.66 to the nearest whole degree: \[ B \approx 39^\circ \]

Final Answer

The approximate measure of angle $ B $ is $ 39^\circ $.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!