from a point 35 meter from a building and 2 meter above the ground, the angle of the elevation of the top of the building is observed to be 60 degrees. what is the height of the building?
find the altitude of an equilateral triangle each of whose sides is 100 cm. long.
as always, draw a diagram. If the building's height is h, then you can see that
(h-2)/35 = tan 60°
If you draw an equilateral triangle, and drop an altitude to one side, you have a 30-60-90 triangle, whose sides are in the ratio 1:√3:2.
You know that the hypotenuse is 100, so now you can find the altitude.
To solve this problem, we can use trigonometry and consider the right triangle formed by the point observer, the top of the building, and the point where the observer is standing.
Let's label the height of the building as 'h'.
We are given the following information:
- The distance between the point observer and the building is 35 meters.
- The height of the observer from the ground is 2 meters.
- The angle of elevation to the top of the building is 60 degrees.
Now, we can use the tangent function to find the height of the building.
Tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, tan(60 degrees) = height of the building / 35 meters.
Mathematically, the equation becomes:
tan(60 degrees) = h / 35
To find h, we can rearrange the equation:
h = 35 * tan(60 degrees)
Using a calculator, we can calculate the value of tan(60 degrees) ≈ 1.732.
Therefore, the height of the building, h = 35 * 1.732 ≈ 60.62 meters.
So, the height of the building is approximately 60.62 meters.