Question

A



26 degree
B 15 C


Use the tangent ratio to solve for missing side length AB of the right triangle.

a. side AB = 6.97
b. side AB = 7.32
c. side AB = 97.03
d. side AB = 30.75

Answer 1

To find the length of side AB in the right triangle using the tangent ratio, we need to set up the problem based on the given angle and the opposite and adjacent sides.

In this scenario, \( \angle A = 26^\circ \), and side BC (the opposite side to angle A) is given as 15. We want to find side AB (the adjacent side to angle A).

Using the tangent ratio:

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

In this case:

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

We can rearrange this to solve for AB:

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

Now, calculating \( \tan(26^\circ) \):

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

Now plug it into the equation:

\[
AB \approx \frac{15}{0.4877} \approx 30.75
\]

The length of side AB is approximately 30.75.

Thus, the correct answer is:

**d. side AB = 30.75**.