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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=30.75
side upper A upper B equals 30.75

side AB=7.32
side upper A upper B equals 7.32

side AB=6.97

Answer 1

To find the length of side AB in right triangle ABC using the tangent ratio, we can use the formula for tangent, which is defined as:

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

In triangle ABC:

• The angle \( C \) is \( 26^\circ \).
• The base (adjacent side) \( AC \) is \( 15 \) units.
• We are looking for the opposite side \( AB \).

Using the tangent ratio:

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

Now we can solve for \( AB \):

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

Now calculating \( \text{tan}(26^\circ) \):

\[ \text{tan}(26^\circ) \approx 0.4877 \]

Now substitute this value into the equation:

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

Rounding to two decimal places:

\[ AB \approx 7.32 \]

Therefore, the correct response is:

side AB = 7.32.