A flag pole and a building stand on the same horizontal level from a point P at the bottom of the building the angle of elevation of the top T of the flag pole is 68 degree.From the top Q of the building the angle of elevation of the point T is 28 degree.If the building is 20m high calculate; distance PT and height of the flag pole
draw a diagram. Review your basic trig functions.
PT cot68 = (PT-20) cot28
I misread the problem. If we label the bottom of the pole B, then
BT cot68 = (BT-20) cot28
Both those expressions give BP, the distance between the building and the pole.
To get PT, then,
PT^2 = BP^2 + BT^2
pls someone should help me solve it
To solve this problem, let's draw a diagram to visualize the situation described.
```
T (top of the flag pole)
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| 68°
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|_________________ P (bottom of the building)
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| 28°
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|
Q (top of the building)
```
From the information given, we know that:
1. The height of the building, PQ, is 20m.
To find the height of the flagpole and the distance PT, we can use the concept of trigonometry.
First, let's find the height of the flagpole:
Step 1: Find the length of PQ (height of the building)
Since the angle of elevation from point Q to point T is 28°, we can use the tangent function:
tan(28°) = PQ / PT
Step 2: Solve for PQ
To find the height of the building, we can multiply PT by the tangent of 28°.
PQ = PT * tan(28°)
Now, let's calculate the height of the flagpole:
Step 3: Find the length of PT (distance between point P and T)
Since the angle of elevation from point P to point T is 68°, we can use the tangent function:
tan(68°) = PQ / PT
Step 4: Solve for PT
To find the distance PT, divide PQ by the tangent of 68°.
PT = PQ / tan(68°)
Calculating the values:
Step 1: PQ = PT * tan(28°)
Step 2: PQ = PT * 0.5317 (approximate value of tan(28°))
Step 3: PT = PQ / tan(68°)
Step 4: PT = PQ / 2.4951 (approximate value of tan(68°))
Substituting the value of PQ from Step 2 into Step 4:
PT = (PT * 0.5317) / 2.4951
Now we can solve this equation:
2.4951 * PT = 0.5317 * PT
Divide both sides by PT:
2.4951 = 0.5317
This equation is not consistent, which means there is no specific solution for the distance PT. There might be an error in the given values or calculations.
However, we can still find the height of the flagpole using the value of PQ calculated through Step 2:
PQ = PT * 0.5317
PQ = 20m * 0.5317
PQ ≈ 10.634m
Hence, the height of the flagpole is approximately 10.634m.