A road runs from the base of a mountain. From two points 235 meters apart on the road, the angles of elevation to the top of the mountain are 43 and 30. how high above the road is the mountaintop?
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To find the height of the mountaintop above the road, we can use trigonometry and set up a right triangle.
Let's call the distance from one of the points on the road to the mountain base point A and the other point on the road point B. The distance between A and B is given as 235 meters.
Now, let's consider the right triangle formed by the road, the mountaintop, and the line of sight from point A to the mountaintop. We can label the height of the mountaintop as h.
From point A, the angle of elevation to the top of the mountain is given as 43 degrees, and from point B, the angle of elevation is given as 30 degrees.
Using the tangent ratio, we can set up the following equations:
tan(43) = h / AB
tan(30) = h / AB
Since AB is the same for both equations, we can equate the two expressions:
h / AB = tan(43) = tan(30)
Now we can solve for the height (h):
h = AB * tan(43) = 235 * tan(43) = approximately 233.34 meters
Therefore, the height of the mountaintop above the road is approximately 233.34 meters.