Two buildings with flat roofs are 60 m apart. From the roof of the
shorter building, 40 m in height, the angle of elevation to the edge of
the roof of the taller building is 40°. How high is the taller building?
Provide an Illustration.
To solve this problem, we can use trigonometry, specifically the tangent function. We will start by drawing a diagram to understand the situation better.
First, draw two buildings with flat roofs, 60 m apart. Label the shorter building with a height of 40 m and the taller one with an unknown height (let's call it "h").
Next, draw a line from the top of the shorter building to the top edge of the taller building's roof. This line represents the line of sight and the angle of elevation, which is given as 40°.
To find the height of the taller building, we need to determine the length of the line segment from the top of the shorter building to the top edge of the taller building's roof.
Now, let's consider the right triangle formed by the shorter building, the taller building, and the line of sight.
In this triangle, the side adjacent to the angle of elevation is the horizontal distance between the buildings, which is 60 m.
The side opposite to the angle of elevation is the height of the shorter building, which is 40 m.
The side we are interested in is the height of the taller building, which we'll call "h".
Using the tangent function, we can set up the following equation:
tan(40°) = h / 60
Now, let's solve for "h".
Multiply both sides of the equation by 60:
h = 60 * tan(40°)
Using a scientific calculator, calculate the value of tan(40°):
h = 60 * 0.8391
Finally, multiply 60 by 0.8391 to find the height of the taller building:
h ≈ 50.35 m
Therefore, the height of the taller building is approximately 50.35 m.
Illustration:
/
/|
/ |
/ |
/ |
/ |
/ 40 | h
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60
In this illustration, the shorter building is on the left, and the taller building is on the right. The angle of elevation (40°) is indicated, and the heights of the buildings are labeled as 40 m and "h" respectively. The horizontal distance between the buildings is 60 m.