Question

triangle:
37 degree
9 adjacent
x opposite

tan (37) = x/9
9 * tan (37) = x
6.78 = x
x = 6.78

What is the correct answer?

a. x = 5.42
b. x = 6.78
c. x = 7.19
d. x = 6.26

Answer 1

Let's verify your calculation step by step.

You used the tangent function correctly. The formula for tangent in a right triangle is:

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

In your case, you have:

\[
\tan(37^\circ) = \frac{x}{9}
\]

To solve for \(x\), you multiplied both sides by 9:

\[
x = 9 \cdot \tan(37^\circ)
\]

Now, let's calculate \(\tan(37^\circ)\):

Using a calculator:
\[
\tan(37^\circ) \approx 0.7536
\]

Now substituting that value in:

\[
x = 9 \cdot 0.7536 \approx 6.7824
\]

When rounded, this result is approximately 6.78.

Looking at the options you provided:

a. x = 5.42
b. x = 6.78
c. x = 7.19
d. x = 6.26

The closest answer based on your calculations is **b. x = 6.78**. Thus, your calculation appears to be correct.