Find to the nearest meter the height of a building if its shadow is 42 meters long when the angle of elevation of the sun measures 42°
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To find the height of the building, we can use trigonometry. We have the length of the shadow (42 meters) and the angle of elevation of the sun (42 degrees).
First, let's define some variables. Let h be the height of the building and let d be the distance from the base of the building to the tip of the shadow.
We can set up a right-angled triangle with the height of the building, the length of the shadow, and the angle of elevation.
Using the tangent function, we have:
tan(42°) = h / d
To solve for h, we need to find the value of d. We can use the sine function for this:
sin(42°) = h / 42
By rearranging the equations, we can solve for h:
h = d * tan(42°)
h = 42 * sin(42°)
Calculating each part:
h ≈ 42 * 0.6691
h ≈ 28.08 meters
Therefore, the height of the building, rounded to the nearest meter, is approximately 28 meters.