Question

Use the tangent ratio to solve for missing side length AB of the right triangle.
Side AC: 26 degrees
Side BC: 15
Side AB: ???

Answer 1

To solve for the missing side length \( AB \) in the right triangle using the tangent ratio, we can set up the relationship based on the definition of the tangent function. The tangent of an angle in a right triangle is equal to the ratio of the length of the opposite side to the length of the adjacent side.

In your case:

- Angle \( A \) (which is \( 26^\circ \))
- Side \( BC \) (the opposite side) = 15
- Side \( AB \) (the adjacent side) = ???

Using the tangent function:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}}
\]

Substituting in the known values:
\[
\tan(26^\circ) = \frac{BC}{AB} = \frac{15}{AB}
\]

To find \( AB \), we can rearrange the equation:
\[
AB \cdot \tan(26^\circ) = 15
\]
\[
AB = \frac{15}{\tan(26^\circ)}
\]

Now, calculate \( \tan(26^\circ) \) using a calculator (ensure it’s set to degrees):
\[
\tan(26^\circ) \approx 0.4877
\]

Now substitute this value into the equation:
\[
AB = \frac{15}{0.4877} \approx 30.73
\]

Therefore, the length of side \( AB \) is approximately \( 30.73 \) units.