From a window of one building,the angle of depression to the base of the second building is 29°30'.If the building are 200 m apart,How high is the second building?
Impossible to say how high the 2nd building is, since all we have is a sight line to its base.
All we really know is that the height h of the window can be found using
h/200 = tan 29°30'
To find the height of the second building, we can use trigonometry.
Let's label the following information:
- Angle of depression: θ = 29°30' = 29.5°
- Distance between the buildings: D = 200 m
We need to find the height of the second building, which we can call h.
In a right triangle formed by the two buildings and the line of sight from the window to the base of the second building, the tangent of the angle of depression is defined as the ratio of the opposite side to the adjacent side:
tan(θ) = h / D
Rearranging the equation, we get:
h = D * tan(θ)
Plugging in the values, we have:
h = 200 * tan(29.5°)
Calculating the value:
h ≈ 114.21 m
Therefore, the height of the second building is approximately 114.21 meters.
To find the height of the second building, we can use trigonometry. Let's break down the problem and the steps to solve it:
1. Visualize the situation: Imagine two buildings standing next to each other, with a horizontal distance of 200 meters between them. From the window of the first building, you see the base of the second building at an angle of depression of 29°30'.
2. Draw a diagram: Sketch a simple diagram representing the two buildings. Label the distance between them as 200 meters and mark the angle of depression as 29°30'.
3. Identify the trigonometric relationship: In this case, we have an angle of depression, which means we need to use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
4. Set up the equation using tangent: Let's denote the height of the second building as "h". The opposite side is "h" (the height) and the adjacent side is 200 meters (the distance between the buildings). So, we have the equation: tan(29°30') = h / 200.
5. Solve the equation: To solve for "h", we need to isolate it. Multiply both sides of the equation by 200 to get rid of the denominator: 200 * tan(29°30') = h. Use a calculator to find the value of tan(29°30'), which is approximately 0.567. Now, multiply 200 by 0.567 to get the height of the second building: h ≈ 113.4 meters.
Therefore, the height of the second building is approximately 113.4 meters.