A lamppost casts a shadow of a man who is standing 15 feet away from the lamppost. The shadow is 5 feet long. The angle of elevation from the tip of the shadow to the lamp is 50. To the nearest foot, the lamppost is _____ feet tall.
(Points : 2)
As always, draw a diagram. Now, recalling your trig functions, it is easy to see that
h/(15+5) = tan 50°
now, just solve for h
55 feet
24 feet, because if you solve for h like Steve said, that's your result
To calculate the height of the lamppost, we can use the trigonometric relationship tangent (tan) which is defined as the opposite side (in this case the height of the lamppost) divided by the adjacent side (in this case the distance from the man to the lamppost).
We are given that the length of the man's shadow is 5 feet and the distance from the man to the lamppost is 15 feet.
To find the height of the lamppost, we can create a right triangle where the height of the lamppost is the opposite side, the distance from the man to the lamppost is the adjacent side, and the angle of elevation is the angle.
Using the formula for tangent:
tan(angle) = opposite / adjacent
tan(50) = height / 15
Now, we can solve for the height by multiplying both sides of the equation by 15:
15 * tan(50) = height
Using a calculator to evaluate the tangent of 50 degrees, we get:
15 * 1.1918 = height
So, the height of the lamppost to the nearest foot is:
height ≈ 17.88 feet
Therefore, the lamppost is approximately 18 feet tall.