From a point 5m. above the water surface, the angle of elevation of the top of a certain tree is 40°10' while the angle of depression to the foot of the tree is 63°20'. Find the height of the tree and the distance from the point of observation.

-Complete Solution Please.

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Tan63.33 = Y1/X = 5/X

X*Tan63.33 = 5
X = 5/Tan63.33 = 2.51 m = Distance from
the point of observation.

Tan40.17 = Y2/X = Y2/2.51
Y2 = 2.51*Tan40.17 = 2.12 m.

h = Y1+Y2 = 5 + 2.12 = 7.12 m.

To find the height of the tree and the distance from the point of observation, we can use trigonometric principles.

Let's start by labeling the relevant information:

- The height of the observer above the water surface: 5m
- The angle of elevation to the top of the tree: 40°10'
- The angle of depression to the foot of the tree: 63°20'

Now, let's solve for the height of the tree:

Step 1: Convert the angle measurements from degrees, minutes, and seconds (DMS) to decimal degrees.

In decimal degrees:
- Angle of elevation: 40.10°
- Angle of depression: 63.33°

Step 2: Use the tangent function to find the distance from the observer to the tree.

Using the angle of depression, we can set up the following equation:
tan(63.33°) = height of the tree / distance from the observer to the tree

Step 3: Solve for the distance from the observer to the tree.

distance from the observer to the tree = height of the tree / tan(63.33°)

Step 4: Substitute the value for the height of the tree.

Let's assume the height of the tree is "h" meters.
Therefore, distance from the observer to the tree = h / tan(63.33°)

Step 5: Use the tangent function to find the height of the tree.

Using the angle of elevation, we can set up the following equation:
tan(40.10°) = height of the tree / distance from the observer to the tree

Step 6: Solve for the height of the tree.

height of the tree = distance from the observer to the tree * tan(40.10°)

Now, let's substitute the values and calculate the height of the tree and the distance from the point of observation:

distance from the observer to the tree = h / tan(63.33°)
height of the tree = distance from the observer to the tree * tan(40.10°)

Once you substitute the values and perform the calculations, you will find the height of the tree and the distance from the point of observation.