A photogrpaher points a camera at a windows in a nearby building forming an angle of 42 degrees with the camera platform. If the camera is 52 meters from the building , how high above the platform is the window, to the nearest hundreth of a meter.
The answer is 46.82m, i would like to the steps/work for getting this answer...thanks in advance
Draw a rt triangle and label the hor side 52m. Label the ver side h; and
label the angle between the hor side
and hyp. 42 deg.
tan42 = h/52,
Cross multiply:
h = 52*tan42 = 46.82m.
To find the height of the window above the platform, we can use trigonometry. Let's break down the problem step by step:
Step 1: Draw a diagram:
Draw a right-angled triangle where the camera position is at the right-angle vertex, the distance from the camera to the building is the base, and the height of the window above the platform is the opposite side.
Step 2: Identify the given values:
Given:
- The angle formed between the camera direction and the building is 42 degrees (let's call it angle A).
- The distance from the camera to the building is 52 meters (let's call it side B).
Step 3: Identify the unknown value:
We need to find the height of the window above the platform (let's call it side C).
Step 4: Determine the trigonometric relationship:
The trigonometric function that relates the angle A, the opposite side (C), and the hypotenuse (B) is the sine function:
sin(A) = opposite / hypotenuse (sin(A) = C / B)
Step 5: Solve for the unknown value:
Rearrange the formula above to solve for C:
C = B * sin(A)
Step 6: Plug in the values and calculate:
C = 52 * sin(42 degrees)
C ≈ 52 * 0.6691
C ≈ 34.7 meters
The height of the window above the platform is approximately 34.7 meters.
To find the height of the window above the platform, we can use trigonometry. Specifically, we can use the tangent function.
Let's define our variables:
- Let "h" be the height of the window above the platform.
- Let "d" be the distance from the camera to the building.
- Let "θ" be the angle between the camera platform and the line of sight to the window.
Given:
- The angle θ is 42 degrees.
- The distance d is 52 meters.
Now, we can use the tangent function to solve for the height h.
tan(θ) = opposite/adjacent
In this case, the opposite side is the height h and the adjacent side is the distance d.
So, we have:
tan(42°) = h/52
Now, let's solve for h.
h = 52 * tan(42°)
Using a calculator, we find:
h ≈ 46.82 meters
Therefore, the height of the window above the platform is approximately 46.82 meters.