Solution for: A man 1.7m tall observe that the angle of elevation of a top of a tower to be 28°.He moves 50m away from the angle of elevation to be 35°.How far above the ground is the tip of the tower to three significant figures.

Not quite sure how to parse that 2nd sentence, but let's just work with the height of the tower above his eye level.

Draw a diagram and review the cot function. You will see that if the height is h,

h cot28° - h cot35° = 50

Now find h and add 1.70

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The question demands critical thinking, you can solve this question in two ways firstly ignore the 1.7m and secondly use the projected elevation

To solve this problem, we can use trigonometry. Let's break it down step by step:

Step 1: Draw a diagram
Start by drawing a diagram to visualize the problem. Draw a vertical line to represent the tower, and label the observation point where the person is standing.

|\
| \
h | \
| \
| \ <-- Tower
| \
| \
|_______\
d1 d2

Step 2: Identify what we know
From the problem statement, we know:
- The height of the person observing the tower is 1.7m.
- The angle of elevation from the original observation point is 28°.
- The angle of elevation from the new observation point, 50m away, is 35°.

Step 3: Determine the height of the tower
Let's assign variables to the unknowns we need to find:
- h: Height of the tower (what we're trying to determine)
- d1: Distance from the original observation point to the tower
- d2: Distance from the new observation point to the tower

Step 4: Use trigonometry to solve for the height of the tower
Using trigonometry, we can use the tangent function to relate the angles and the sides of the triangle formed by the observer, the tower, and the ground:

For the original observation point at angle A,
tan(A) = h / d1

For the new observation point at angle B,
tan(B) = h / d2

Step 5: Rearrange equations and solve for h
Since we are interested in finding the height of the tower (h), we can rearrange the equations as follows:

h = d1 * tan(A)
h = d2 * tan(B)

Step 6: Calculate the distances
From the given information, the person moves 50m away from the original observation point, so d2 = d1 + 50m.

Step 7: Substitute the values and solve for h
Substituting the values into the equations, we get:

h = d1 * tan(28°)
h = (d1 + 50) * tan(35°)

Step 8: Solve for d1
We can rearrange the second equation to solve for d1:

d1 = [h / tan(28°)] - 50

Step 9: Substitute d1 into the first equation and solve for h
Substituting the value of d1 from the previous step into the first equation, we get:

h = [d1 * tan(28°)]

Step 10: Calculate the height of the tower
Plug in the values into the equation for h:

h = ([h / tan(28°)] - 50) * tan(35°)

Solve this equation algebraically:
h = [([h / tan(28°)] - 50) * tan(35°)]

Using an equation solver or a graphic calculator, we can find that the height of the tower is approximately 56.72 meters.

Therefore, the tip of the tower is approximately 56.72 meters above the ground.