At a distance of 100 feet, the angle of elevation from the horizontal ground to the top of a building is 42 degrees. Find the height of the building
To find the height of the building, we can use trigonometry. In this case, we have the angle of elevation and the distance from the observer to the base of the building.
We can use the tangent function, which relates the angle of elevation (in this case, 42 degrees) to the opposite side length (height of the building) and the adjacent side length (distance from the observer to the base of the building).
Tangent of an angle = opposite side / adjacent side
Let's denote the height of the building as 'h' and the distance from the observer to the base of the building as 'd'. We have the following information:
Angle of elevation = 42 degrees
Distance from the observer to the base of the building = 100 feet
Using the tangent function:
tan(42 degrees) = h / d
We can rearrange the equation to solve for the height of the building:
h = d * tan(42 degrees)
Now we can substitute the given values into the equation:
h = 100 feet * tan(42 degrees)
Calculating the value:
h = 100 feet * 0.9004
Therefore, the height of the building is approximately 90.04 feet.
tan 42 = h/100
so
h = 100 tan 42
h/100 = tan42°
h=90