A point is directly below a window. Another point B is 15 m from A and at the same horizontal level. From B angle elevation of the top of the bottom of the window is 300 and the angle elevation of the top of the widow is 350. Calculate the vertical distance.
(a) From A to the bottom of the window
(b) From the bottom to top of the window.
The exposition is rather garbled, but I take it that
A is x below the window
The window has height h
x/15 = tan 5°
(x+h)/15 = tan 35°
Now you can answer the questions. (I think)
Student
Answer me
To calculate the vertical distances, we can use trigonometric functions. Let's solve each part step by step:
(a) From A to the bottom of the window:
1. Draw a diagram to visualize the problem: Draw a horizontal line to represent the ground, a vertical line for the window, and label the points A and B accordingly.
2. Identify the given angles and distances:
- The angle of elevation from point B to the bottom of the window is 30° (as given).
- The angle of elevation from point B to the top of the window is 35° (as given).
- The distance between points A and B is 15 m (as given).
3. Determine the horizontal distance from point B to the window:
Since the horizontal level is the same between points A and B, the horizontal distance between them is directly equal to the distance between A and B, which is 15 m.
4. Calculate the vertical distance (height) from point A to the bottom of the window:
We can use the trigonometric function tangent (tan) to solve for this. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
tangent(30°) = height / 15 m
Rearranging the equation, we have:
height = tangent(30°) * 15 m
Use a scientific calculator to find the tangent of 30°, which is approximately 0.5774.
height ≈ 0.5774 * 15 m ≈ 8.66 m
Therefore, the vertical distance from A to the bottom of the window is approximately 8.66 meters.
(b) From the bottom to the top of the window:
1. We already know the height from A to the bottom of the window is 8.66 m (from part a).
2. Calculate the additional vertical distance from the bottom to the top of the window:
Since the angle of elevation from B to the top of the window is 35°, we can apply the same steps as in part a.
tangent(35°) = additional height / 15 m
Rearranging the equation, we have:
additional height = tangent(35°) * 15 m
Using a scientific calculator, find the tangent of 35°, which is approximately 0.7002.
additional height ≈ 0.7002 * 15 m ≈ 10.50 m
Therefore, the vertical distance from the bottom to the top of the window is approximately 10.50 meters.