from 25 feet away from the base of a building, the angle of elevation from the ground to the top of a building is measured 38 degrees. how tall is the building. WHat i did was put 25 feet on the base of the triangle the angle measurement oppsite and the longer leg x is this correct
19.53 or 19.5
not sure just what you did, but if the height is x, then
x/25 = tan 38°
Actually, x is the shorter leg. The 38° angle is from the ground to the top of the building.
Yes, you are on the right track. To solve the problem, you can use the tangent function, which relates the angle of elevation to the height of the building.
Let's label the angle of elevation as θ, the distance from the base to the building as x, and the height of the building as h.
We can set up the following equation using the tangent function:
tan(θ) = h / x
In this case, the angle of elevation is given as 38 degrees and the distance from the base to the building is 25 feet. Plugging these values into the equation, we get:
tan(38) = h / 25
Now, we can solve for h:
h = tan(38) * 25
Using a scientific calculator or an online calculator, you can find the tangent of 38 degrees. It is approximately 0.7813. Plugging this value into the equation, we have:
h = 0.7813 * 25
Calculating this, we find:
h ≈ 19.53 feet
Therefore, the height of the building is approximately 19.53 feet.
Yes, that is the correct approach to solve the problem. You have correctly identified the base of the triangle as 25 feet and the angle of elevation as 38 degrees. The longer leg of the triangle represents the height of the building, which is what you need to find.
To calculate the height of the building, you can use trigonometric functions. In this case, you can use the tangent function (tan) because you have the opposite side (height) and the adjacent side (base).
Here's how you can proceed:
1. Set up the equation using the tangent function:
tan(angle) = opposite/adjacent
In this case, the angle is 38 degrees, the opposite side is the height of the building (which we'll denote as x), and the adjacent side is the base of the triangle, which is 25 feet.
tan(38 degrees) = x/25
2. Solve for x:
Multiply both sides of the equation by 25 to isolate x:
x = 25 * tan(38 degrees)
3. Calculate the value of x:
Using a scientific calculator or trigonometric table, find the tangent of 38 degrees:
tan(38 degrees) ≈ 0.78129
Multiply 25 by the tangent value to get the height of the building:
x ≈ 25 * 0.78129 ≈ 19.53 feet
So, the height of the building is approximately 19.53 feet.