About how tall is a tower i f the angle of depression from its top to a point 75 metres from the base is 62 degrees?
To find the height of the tower, we can use trigonometric functions and the information given.
First, let's define the variables:
h = Height of the tower (what we want to find)
d = Distance from the base of the tower to the point where the angle of depression is being measured (75 metres in this case)
θ = Angle of depression (62 degrees in this case)
Now we can use trigonometry to solve for the height.
In a right triangle, the tangent function can help us relate the angle of depression to the height and the distance. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
tangent(θ) = opposite / adjacent
tangent(62 degrees) = h / d
Since we are given the values for the angle and the distance, we can substitute them into the equation and solve for the height:
tangent(62 degrees) = h / 75
To find the height, we isolate 'h' by multiplying both sides of the equation by 75:
h = 75 * tangent(62 degrees)
Now we can calculate the height using a calculator:
h = 75 * 1.880726465
Rounding to the nearest meter, the height of the tower is approximately 141 meters.