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A surveyor is trying to find the height of a hill. The angle of elevation is 45° from the top and 20° from a point 250 meters away. Find the height of the hill.

a) 125 meters
b) 250 meters
c) 375 meters
d) 500 meters

1 Answer

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Final answer:

To find the height of the hill, you can use trigonometry to set up two equations and solve them simultaneously. The height of the hill is approximately c) 375 meters.

Step-by-step explanation:

To find the height of the hill, we can use trigonometry. Let's call the height of the hill H. We have two angles of elevation: one is 45° from the top and the other is 20° from a point 250 meters away.

We can use the tangent function to set up two equations:

tan(45°) = H / x, where x is the distance from the top to the point 250 meters away.

tan(20°) = H / (x + 250), where x + 250 is the total distance from the point of reference to the top of the hill.

By substituting the values into the equations and solving them simultaneously, we can find the height of the hill H.

The height of the hill is approximately 375 meters (Option c).

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