Question

Use the tangent ratio to solve for missing side length AB of the right triangle. Length BC is 15 and angle C is 26 degrees.
side AB = 7.32 side AB = 97.03 side AB = 30.75 side AB = 6.97

Answer 1

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

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

In this triangle, we have:

- Angle \( C = 26^\circ \)
- Side \( BC = 15 \) (which is the side adjacent to angle \( C \))
- Side \( AB \) (which is opposite angle \( C \))

Using the tangent function:

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

Substituting the known values:

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

To find \( AB \):

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

Now, we can calculate \( \tan(26^\circ) \). Using a calculator, we find:

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

Now, substituting this back into the equation:

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

Rounding to two decimal places:

\[
AB \approx 7.32
\]

Therefore, the length of side AB is **7.32**.