Right triangle A B C has a base of 15. Angle C is labeled 26 degrees.

Question

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