A surveyor measures the angle from his location to the top of cliff to be 51 degrees.If he is standing 100m from the base of the cliff, how high is it?
Anyone have any idea how to do this porblem?
draw the diagram. H/Base= tan51, solve for H.
To solve this problem, we can use trigonometry, specifically the tangent function.
Let's label the height of the cliff as "h". Since we know the distance from the base of the cliff to the surveyor is 100m, we can label this as "d". We also know the angle between the surveyor's line of sight and the ground, which is 51 degrees.
The tangent function relates the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the height of the cliff (h) and the adjacent side is the distance from the base of the cliff to the surveyor (d).
Therefore, we can set up the following equation:
tan(51) = h / d
To solve for h, we need to isolate it on one side of the equation. Multiply both sides of the equation by "d":
tan(51) * d = h
Now, we can substitute the given values:
h = tan(51) * 100
Using a calculator, find the tangent of 51 degrees (tan(51)), and then multiply it by 100:
h ≈ tan(51) * 100
Using a scientific calculator, the answer should be approximately:
h ≈ 137.35 meters
So the height of the cliff is approximately 137.35 meters.