Question

use the tangent ratio to solve for missing side length AB of the right triangle. Round to the nearest hundreths (2 decimal places)


B is thr right angle
the distance of BC is 15
C is 26 degrees

Answer 1

this is incorrect

Answer 2

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In your triangle:

- Angle C is 26 degrees.
- Side BC (the opposite side to angle C) is 15.
- Side AB (the adjacent side to angle C) is what we are trying to find.

Using the tangent ratio:

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

Substituting the known values:

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

This simplifies to:

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

Now, we can rearrange this equation to solve for \( AB \):

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

Next, we need to calculate \( \tan(26^\circ) \). Using a calculator, we find:

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

Now substitute this value back into the equation:

\[
AB = \frac{15}{0.4877} \approx 30.73
\]

Rounding to the nearest hundredths, the length of side AB is:

\[
\boxed{30.73}
\]

Answer 3

I apologize for any confusion. Let's go through the calculations step-by-step to ensure accuracy.

### Given:
- Angle \( C = 26^\circ \)
- Side \( BC \) (opposite side) = 15
- Side \( AB \) (adjacent side) = ?

### Using the Tangent Ratio:
The tangent of angle \( C \) is defined as:

\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AB}
\]

Plugging in the values we have:

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

### Rearranging to find \( AB \):

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

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

### Calculating \( \tan(26^\circ) \):

Using a calculator, we find:

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

### Calculate \( AB \):

\[
AB = \frac{15}{0.4877} \approx 30.73
\]

However, if you believe this is incorrect, I think there may have been a misunderstanding about which side is opposite and which is adjacent.

### Re-examining \( BC \):

If \( BC \) is the adjacent side and we are trying to find \( AB \) as the opposite side, we should set it up like this:

1. If \( AB \) is the opposite side, and \( BC \) is actually adjacent, the equation would be:
\[
\tan(26^\circ) = \frac{AB}{15}
\]
Rearranging gives:
\[
AB = 15 \cdot \tan(26^\circ)
\]

Now, calculating this correctly:

\[
AB = 15 \cdot \tan(26^\circ) \approx 15 \cdot 0.4877 \approx 7.31
\]

### Final Answer:
So if we are solving for the side opposite to the 26-degree angle \( (AB) \):

\[
AB \approx 7.31
\]

Rounded to the nearest hundredths, the correct length of side \( AB \) is:

\[
\boxed{7.31}
\]

If the configuration was intended differently, please provide more context or corrections. Thank you for your patience!