Question

Solve for x. Round to the nearest tenth of a degree, if necessary.
Hypotenuse = 6
Opposite = 3.3
X = ?

Answer 1

To find the angle \( x \) in a right triangle where the length of the hypotenuse is 6 and the length of the opposite side is 3.3, we can use the sine function defined in a right triangle:

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

Substituting the known values:

\[
\sin(x) = \frac{3.3}{6}
\]

Calculating the right-hand side:

\[
\sin(x) = 0.55
\]

To find \( x \), we need to take the inverse sine (arcsin) of 0.55:

\[
x = \arcsin(0.55)
\]

Using a calculator to find this value:

\[
x \approx 33.6^\circ
\]

Rounding to the nearest tenth of a degree:

\[
\boxed{33.6^\circ}
\]