Question

Draw a sketch of this question ; the angle of elevation of x from y is 30degree. If |xy|=40m how high is x above the level of y

Answer 1

To sketch this scenario, follow these steps:

1. **Draw a horizontal line** to represent the level of point Y. Label this line as the ground level.

2. **Place point Y** on the left side of the horizontal line. This is the point from which the angle of elevation is measured.

3. **From point Y**, draw a line at an angle of 30 degrees above the horizontal line towards point X. This line represents the line of sight from Y to X.

4. **Mark the point X** somewhere above the horizontal line along the line of sight from Y.

5. **Draw a vertical line** from point X down to the horizontal line (ground level), and label this line as the height (h) from Y to X.

6. **Label the distance |XY|** as 40 meters along the line of sight (the hypotenuse of the triangle formed by Y, X, and the point directly below X on the ground).

Now, to find the height of X above the level of Y, you can use trigonometry. Specifically, you can use the sine function:

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

For this problem:

- \(\theta = 30^\circ\)
- The opposite side (height) is what we want to find, let's call it \(h\).
- The hypotenuse |XY| is 40 m.

Using the sine function:

\[
\sin(30^\circ) = \frac{h}{40}
\]

Since \(\sin(30^\circ) = \frac{1}{2}\):

\[
\frac{1}{2} = \frac{h}{40}
\]

Now, solving for \(h\):

\[
h = 40 \times \frac{1}{2} = 20 m
\]

Thus, point X is 20 meters above the level of point Y.

You can visualize this setup by imagining a right triangle where:
- The angle at Y is 30 degrees,
- The hypotenuse (|XY|) is 40 m,
- The vertical height (h) from Y to X is 20 m.