Question

Right triangle A B C has a base of 15. Angle C is labeled 26 degrees.
Use the tangent ratio to solve for missing side length AB of the right triangle.

(1 point)
Responses

side AB=97.03
side upper A upper B equals 97.03

side AB=6.97
side upper A upper B equals 6.97

side AB=7.32
side upper A upper B equals 7.32

side AB=30.75

Answer 1

To find the length of side AB using the tangent ratio in triangle ABC, we can set up the following relationship:

\[
\tan(C) = \frac{\text{opposite side}}{\text{adjacent side}}
\]

In triangle ABC:
- The angle C is 26 degrees.
- The opposite side to angle C is side AB.
- The adjacent side to angle C is the base AC, which is given as 15.

Thus, we can set up the equation:

\[
\tan(26^\circ) = \frac{AB}{15}
\]

To solve for side AB, we rearrange the equation:

\[
AB = 15 \cdot \tan(26^\circ)
\]

Now, we need to calculate \( \tan(26^\circ) \):

- Using a calculator, we find:

\[
\tan(26^\circ) \approx 0.4877
\]

Substituting this value back into the equation for side AB:

\[
AB \approx 15 \cdot 0.4877 \approx 7.315
\]

Rounding this value gives us:

\[
AB \approx 7.32
\]

Thus, the correct answer is:

**side AB = 7.32**