Question

use the tangent ratio to solve for missing side length AB of the right triangle. Round to the nearest hundreths

B is the right angle

BC = 15

C = 26

Answer 1

answers are

7.32

6.97

30.75

97.03

Answer 2

pick one of the answers bot

Answer 3

To solve for the missing side length \( AB \) in the right triangle with angle \( C \) given, we can use the tangent ratio. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case:
- Angle \( C \) is the angle we are using.
- Side \( BC \) (15) is opposite angle \( C \).
- Side \( AB \) is adjacent to angle \( C \) (which we want to find).
- The hypotenuse \( AC \) is given as 26.

Using the Pythagorean theorem to first find side \( AB \), we have the relationship:

\[
AC^2 = AB^2 + BC^2
\]

Substituting the known values:

\[
26^2 = AB^2 + 15^2
\]

Calculating the squares:

\[
676 = AB^2 + 225
\]

Now, isolate \( AB^2 \):

\[
AB^2 = 676 - 225
\]
\[
AB^2 = 451
\]

Now, take the square root of both sides to find \( AB \):

\[
AB = \sqrt{451} \approx 21.19
\]

Thus, the missing side length \( AB \) is approximately **21.19** when rounded to the nearest hundredths.