Two buildings with flat roofs are 60m apart. From the roof of the shorter building, 40m in height, the angle of elevation to the edge of the roof of the taller bldg. is 40°. How high is the taller bldg.?
h = 40 + 60tan40°
Well, if we're talking about tall buildings, I hope they're not skyscrapers for giraffes! Anyway, let's solve this like a puzzle.
We have a shorter building with a height of 40m. The angle of elevation to the edge of the taller building's roof is 40°. So, we can use some trigonometry here.
Let's call the height of the taller building 'h'. Now, if we draw a triangle, we have the opposite side, which is the height of the shorter building (40m), and we have the angle of 40°.
Using the tangent function (opposite/adjacent), we get:
tan(40°) = 40m/h
Now, let's solve for 'h':
h = 40m / tan(40°)
Calculating that, we find that the height of the taller building is approximately 48.15m. So, the punchline is, the taller building is reaching new heights at 48.15m!
To find the height of the taller building, we can use trigonometry based on the given information.
Let's denote the height of the taller building as 'h'.
From the shorter building, the angle of elevation to the edge of the roof of the taller building is 40°. This means that if we draw a right-angled triangle with the shorter building roof edge and the taller building roof edge, the angle between the ground and the line joining the shorter building roof edge to the taller building roof edge is 40°.
Now, let's consider the right-angled triangle with the following dimensions:
- The side opposite to the angle of elevation is 'h' (height of the taller building).
- The side adjacent to the angle of elevation is 60m (distance between the two buildings).
- The side opposite to the 90° angle (the ground) is 40m (height of the shorter building).
Using trigonometry, specifically using the tangent function (tan), we can relate the angle of elevation to the sides of the right-angled triangle:
tan(angle of elevation) = (opposite side) / (adjacent side)
tan(40°) = h / 60m
Now, let's solve for 'h':
h = tan(40°) * 60m
Using a calculator:
h ≈ 46.36m
Therefore, the height of the taller building is approximately 46.36 meters.
To find the height of the taller building, we can use the trigonometric concept of tangent.
Let's start by drawing a diagram to visualize the situation:
Taller Building (unknown height)
___________________________
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| / 40°
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|______________/
Shorter Building (40m in height)
In this diagram, we have the two buildings, the shorter one with a known height of 40m, and the taller one with an unknown height h (which we need to find).
Now, let's consider the triangle formed by the shorter building, the taller building, and the line of sight from the roof of the shorter building to the edge of the taller building's roof.
The angle of elevation is the angle between the horizontal ground and the line of sight. In this case, the angle of elevation is given as 40°.
Since we are given the height and the angle, we can use the trigonometric formula:
tangent(angle) = opposite/adjacent
or
tan(40°) = 40m/h
Rearranging the formula, we get:
h = 40m / tan(40°)
Now, we can solve for h using a scientific calculator or online calculator:
h ≈ 40m / tan(40°) ≈ 52.8m
Therefore, the height of the taller building is approximately 52.8 meters.