Question

Solve for x. Round to the nearest tenth, if necessary. the hypotenuse is 8.9 the opposite side is x and the angle is 36 degrees

Answer 1

To solve for \( x \) (the length of the opposite side) in a right triangle where the hypotenuse is 8.9 and the angle is 36 degrees, we can use the sine function, which relates the angle to the ratios of the sides of the triangle.

The sine function is defined as:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case, \( \theta = 36^\circ \) and the hypotenuse is 8.9. We can set up the equation as follows:

\[
\sin(36^\circ) = \frac{x}{8.9}
\]

To solve for \( x \), multiply both sides by 8.9:

\[
x = 8.9 \cdot \sin(36^\circ)
\]

Next, we calculate \( \sin(36^\circ) \). Using a calculator:

\[
\sin(36^\circ) \approx 0.5878
\]

Now substitute this value back into the equation:

\[
x \approx 8.9 \cdot 0.5878
\]

Calculating this gives:

\[
x \approx 5.22
\]

Finally, rounding to the nearest tenth:

\[
x \approx 5.2
\]

So, the length of the opposite side \( x \) is approximately **5.2**.