Using basic trig functions solve the following right triangle problem where the angle∠ C = 90degrees°.
Round to one decimal place.
If b = 31 and angle∠ A = 43degrees°, what does a = ?

To solve for \( a \) in a right triangle using trigonometric functions, we can apply the following steps based on the given information:

- \( \angle C = 90^\circ \) (right angle)
- \( \angle A = 43^\circ \)
- \( b = 31 \) (opposite side to \( \angle A \))

We need to find side \( a \), which is adjacent to angle \( A \).

### Step 1: Identify the correct trigonometric function
Since we know the angle \( A \) and the opposite side \( b \), we can use the **tangent** function to relate the sides.

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

For angle \( A \):

\[
\tan(43^\circ) = \frac{31}{a}
\]

### Step 2: Solve for \( a \)

Rearranging the equation to solve for \( a \):

\[
a = \frac{31}{\tan(43^\circ)}
\]

### Step 3: Calculate the value of \( a \)

Using a calculator, we find:

\[
a = \frac{31}{\tan(43^\circ)} \approx \frac{31}{0.9325} \approx 33.2
\]

### Final Answer:
\[
a \approx 33.2
\]

Would you like further details or have any questions?

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Here are 5 related questions to explore:
1. How do you calculate the hypotenuse using trigonometry?
2. What if you were given side \( a \) and angle \( A \)? How would you find side \( b \)?
3. Can you use the sine or cosine functions to solve this problem?
4. How do you determine angle \( B \) in this triangle?
5. What is the Pythagorean theorem and how does it apply here?

**Tip:** When solving right triangles, always double-check which side is opposite, adjacent, or the hypotenuse in relation to the given angle.

Using basic trig functions solve the following right triangle problem where the angle∠ C = 90 degrees°. Round to one decimal place. If b = 31 and angle∠ A = 43 degrees°, what does a = ?

Learn how to solve a right triangle problem using trigonometric functions. Given angle A = 43° and side b = 31, this problem demonstrates how to use the tangent function to find side a. Includes step-by-step calculations and explanations. Perfect for Grades 9-11.

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