From a rock ledge the angle of elevation to the topof a treeis 25 degrees. The angle of depression to the bottom of the tree is 10 degrees. Find the heightof the rock ledgeto the nearest tenth and find the height of the tree to the nearest tenth
The distance is 100m
I response my sister.. And my stud
To solve this problem, we can use trigonometry. Let's denote the height of the rock ledge as "x" and the height of the tree as "h".
First, let's find the height of the rock ledge:
We have the angle of elevation, which is the angle between the line of sight from the rock ledge to the top of the tree and the horizontal. In this case, the angle of elevation is 25 degrees.
Using tangent function, we can write:
tan(25) = x / distance
We don't have the actual distance, but since we only need the height of the rock ledge, it doesn't matter. We can set the distance to any value. Let's set it to 1.
tan(25) = x / 1
x = tan(25)
So, the height of the rock ledge is approximately equal to tan(25).
Next, let's find the height of the tree:
We have the angle of depression, which is the angle between the line of sight from the rock ledge to the bottom of the tree and the horizontal. In this case, the angle of depression is 10 degrees.
Using tangent function again, we can write:
tan(10) = h / distance
As before, we can set the distance to any value. Let's set it to 1.
tan(10) = h / 1
h = tan(10)
So, the height of the tree is approximately equal to tan(10).
To get the final answer, calculate the values of tan(25) and tan(10) using a scientific calculator or online trigonometric calculator. Then round the results to the nearest tenth.
Once you have the values, you will have the height of the rock ledge and the height of the tree to the nearest tenth.
as usual, draw a diagram and recall your basic trig definitions.
If the ledge is at height a, and at distance x from the tree (with height h), then we have
(h-a)/x = tan25°
a/x = tan10°
Now eliminate a to get
h-x tan25° = x tan10°
h = x(tan25°+tan10°)
Now you still have to know how far away the tree is. Naturally, the closer you are, the shorter the actual height, since it just subtends an angle of 35°.