Jacob is standing 112 m from a building. The angle of elevation when he looks up to the top of the building is 62°.
How tall is the building?
Enter your answer, rounded to the nearest tenth
I'm really confused on this question
210.6 just taken the test and that’s the answer.
tan 62 = h/112
so
h = 112 tan 62
To find the height of the building, we can use trigonometry.
We have the opposite side (height of the building) and the adjacent side (distance from Jacob to the building). By using the tangent function, we can find the height.
The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
So, we can use the equation:
tan(angle) = opposite / adjacent
In this case, the angle is 62°, the opposite side is the height we want to find, and the adjacent side is 112 m.
Therefore, the equation becomes:
tan(62°) = height / 112
To find the height, we can rearrange the equation:
height = tan(62°) * 112
Using a calculator, we find:
height ≈ 220.1 m
Therefore, the height of the building is approximately 220.1 meters.
To solve this question, we can use trigonometry, specifically the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Step 1: Identify the known information:
- The distance between Jacob and the building is 112 m.
- The angle of elevation from Jacob to the top of the building is 62°.
Step 2: Determine the appropriate ratio:
Since we are given the angle of elevation and the distance from the building, we need to find the height of the building, which represents the opposite side. Therefore, we will use the tangent function.
Step 3: Set up the equation:
tan(θ) = opposite/adjacent
In this case, θ represents the angle of elevation, so we have:
tan(62°) = opposite/112
Step 4: Solve for the opposite side (height of the building):
To solve for the opposite side, we can rearrange the equation:
opposite = tan(62°) * 112
Step 5: Calculate the height of the building:
Using a calculator, find the tangent of 62° (tan(62°)) and multiply it by 112:
opposite ≈ 2.042035225
Therefore, the height of the building is approximately 2.0 m when rounded to the nearest tenth.