A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 27∘. From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 29∘.
How high (in feet) is the mountain?
review the definition of cot(x). You will see that if the height is h,
h*cot27° - h*cot29° = 1000
To find the height of the mountain, we can use trigonometry and set up a right triangle. Let's label the height of the mountain as 'h', the distance from the first point to the foot of the mountain as 'x', and the distance from the second point to the foot of the mountain as 'x + 1000'.
We can use the tangent function to relate the angle of elevation to the height and distance.
In the first scenario, we have the following equation:
tan(27∘) = h / x
In the second scenario, we have the following equation:
tan(29∘) = h / (x + 1000)
Now, we can solve the system of equations to find the value of 'h'.