Question

Solve for xx. Round to the nearest tenth, if necessary.
O
P
Q
19°
x
33
Answer
Attempt 1 out of 2

p has a 90 degree angle

Answer 1

To solve for \( x \) in triangle OPQ where you have a right angle at P, and given the measurements:

- Angle O = 19°
- Side OP = 33 (adjacent to angle O)
- Side PQ = x (opposite to angle O)

You can use the tangent trigonometric ratio, which relates the opposite side to the adjacent side in a right triangle.

The relationship is given by:

\[
\tan(O) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{33}
\]

Substituting the known angle:

\[
\tan(19°) = \frac{x}{33}
\]

Now, solve for \( x \):

\[
x = 33 \cdot \tan(19°)
\]

Using a calculator to find \( \tan(19°) \):

\[
\tan(19°) \approx 0.3443
\]

Now, calculate \( x \):

\[
x \approx 33 \cdot 0.3443 \approx 11.36
\]

Rounding to the nearest tenth:

\[
x \approx 11.4
\]

Thus, the solution for \( x \) is:

\[
\boxed{11.4}
\]