a tree is situated on level ground from a point 135 feet from the base of the tree the measure of the angle of elevation from the ground to the top of the tree is 43 degrees which is the height of the tree to the nearest foot?
height=tan43*135
fse
obama
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To find the height of the tree, we can use the tangent of the angle of elevation.
Let's label the height of the tree as 'h' (in feet).
The tangent of an angle is equal to the opposite side divided by the adjacent side in a right triangle. In this case, the opposite side is the height of the tree (h), and the adjacent side is the distance from the base of the tree to the point where the angle is measured (which is 135 feet).
So, we can set up the equation:
tan(43 degrees) = h / 135
To find h, we need to solve for it.
Step 1: convert the angle from degrees to radians.
43 degrees = 43 * (π / 180) radians
Step 2: rearrange the equation to solve for h.
h = 135 * tan(43 * (π / 180))
Now we can calculate it using a calculator.
h ≈ 135 * tan(43 * (π / 180))
After evaluating this expression, we get:
h ≈ 135 * tan(0.7505)
h ≈ 135 * 0.9834
h ≈ 132.45
Therefore, the height of the tree is approximately 132.45 feet to the nearest foot.