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

Question

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

Answer 1

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 2

this is incorrect

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!