The point A is directly below a window. Another point B is 15 m from A and at the same horizontal level. From B angle of elevation of the top of the bottom of the window is 300 and the angle of elevation of the top of the window is 350. Calculate the vertical distance.
(a) From A to the bottom of the window (b) From the bottom to top of the window
I guess 360 is straight up ?
tan 30 = h bottom/ 15
tan 80 = h top / 15
To solve this problem, we can use trigonometry. Let's break down the given information:
1. Point A is directly below the window.
2. Point B is 15 meters from A and at the same horizontal level.
3. The angle of elevation from point B to the bottom of the window is 30 degrees.
4. The angle of elevation from point B to the top of the window is 35 degrees.
Let's calculate the vertical distances:
(a) From A to the bottom of the window:
To find this distance, we can use the tangent function since we have the angle and the opposite side (vertical distance). Let's call the vertical distance "x."
In right triangle ABD, the tangent of angle 30 degrees is given by tangent(30°) = x/15.
Rearrange the equation to solve for x: x = 15 * tangent(30°).
Using a scientific calculator, calculate the tangent of 30 degrees: tangent(30°) ≈ 0.577.
Substituting this value into the equation: x ≈ 15 * 0.577.
Calculating further: x ≈ 8.655 meters.
Therefore, the vertical distance from point A to the bottom of the window is approximately 8.655 meters.
(b) From the bottom to the top of the window:
Here, we will use the same logic. Let's call the vertical distance from the bottom to the top of the window as "y".
In right triangle BCD, the tangent of angle 5 degrees is given by tangent(35°) = y/15.
Rearranging the equation: y = 15 * tangent(35°).
Using a scientific calculator, calculate the tangent of 35 degrees: tangent(35°) ≈ 0.700.
Substituting this value into the equation: y ≈ 15 * 0.700.
Calculating further: y ≈ 10.5 meters.
Therefore, the vertical distance from the bottom to the top of the window is approximately 10.5 meters.