Question

The angle of elevation of point P from point Q is 40°,PQ =45km. How high is point P above the level of point Q

Answer 1

To find the height of point P above the level of point Q given the angle of elevation and the distance PQ, we can use trigonometry.

We have:
- The angle of elevation \(\theta = 40^\circ\)
- The distance \(PQ = 45\) km

We want to find the height \(h\) of point P above point Q. We can use the tangent of the angle:

\[
\tan(\theta) = \frac{\text{Opposite side (height)}}{\text{Adjacent side (distance)}}
\]

Rearranging the formula to find the height \(h\):

\[
h = PQ \cdot \tan(\theta)
\]

Now, substituting the values:

\[
h = 45 \cdot \tan(40^\circ)
\]

Calculating \(\tan(40^\circ)\):

Using a calculator, \(\tan(40^\circ) \approx 0.8391\).

Now, calculate \(h\):

\[
h \approx 45 \cdot 0.8391 \approx 37.76 \text{ km}
\]

Thus, the height of point P above the level of point Q is approximately \(37.76\) km.