From a point 35 m from a building and 2 m above the ground , the angle of elevation of the top of the building is observed to be 60° what the height of the building?
draw a diagram
(h-2)/35 = tan60°
if a monument and a building were placed on the circumference of a circle of radius r ft. on level ground, the angles of the elevation of their tops at the center of the circle would be 30 degrees and 60 degrees respectively . find the ratio of their heights?
To find the height of the building, we can use trigonometry. We have the angle of elevation and the distance from the building, which is 35 meters. Let's label the height of the building as "h" (in meters).
First, we need to determine which trigonometric ratio to use. The tangent (tan) function relates the opposite side length (the height of the building "h") to the adjacent side length (the distance from the building "35 m"). So, we can use the tangent function.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the building ("h") and the adjacent side is the distance from the building ("35 m").
The tangent of the angle of elevation (60°) is given by the formula: tan(60°) = h / 35.
Now, we can solve this equation for 'h':
tan(60°) = h / 35
To find the value of tan(60°), you can use a scientific calculator or refer to a trigonometric table. The tangent of 60° is approximately √3 or 1.732.
Substituting this value into the equation:
1.732 = h / 35
To isolate 'h', multiply both sides of the equation by 35:
1.732 * 35 = h
Calculating the left side of the equation:
h ≈ 60.62
Therefore, the height of the building is approximately 60.62 meters.