A flugpole and a building stand on the same horizontal level. From the point P at tue bottom of the building, the angle of elevation of the top of the flogpole is 65 degree from the top Q of the building the angle of elevation of the point T is 25 degree. If the building is 20m high, calculate (a) distance PT (b) Height of the flogpole (c) distance QT
Make your necessary diagram.
Look at triangle PTQ
angle QPT = 25° , since angle of elevation was given as 65°
angle TQP = 115°, which leaves 40° for angle T
by the sine law:
TP/sin115 = 20/sin40
TP = 20sin115/sin40 = ....
but TP is the hypotenuse of the original righ-angled triangle with the flagpole (flogpole, flugpole) as its vertical side, so
sin65° = height of flagpole/TP
height of flagpole = TPsin65 = ...
To solve this problem, we can use trigonometric ratios and create two right triangles. Let's label the points and given values as follows:
P: Point at the bottom of the building
Q: Point at the top of the building
T: Top of the flagpole
Given information:
- Angle of elevation from P to T: 65 degrees
- Angle of elevation from Q to T: 25 degrees
- Height of the building (PQ): 20m
(a) Distance PT:
To find the distance PT, we need to find the length of the side opposite the angle of elevation at point P.
Tan(65°) = Opposite / Adjacent
Tan(65°) = PT / 20m
Using a scientific calculator:
PT = 20m * Tan(65°)
PT ≈ 41.5m
Therefore, the distance PT is approximately 41.5 meters.
(b) Height of the flagpole:
To find the height of the flagpole, we need to find the length of the side opposite the angle of elevation at point Q.
Tan(25°) = Opposite / Adjacent
Tan(25°) = Height of the flagpole / 20m
Using a scientific calculator:
Height of the flagpole = 20m * Tan(25°)
Height of the flagpole ≈ 8.74m
Therefore, the height of the flagpole is approximately 8.74 meters.
(c) Distance QT:
To find the distance QT, we can use the height of the flagpole we just calculated and the given height of the building.
QT = Height of the flagpole + Height of the building
QT = 8.74m + 20m
QT ≈ 28.74m
Therefore, the distance QT is approximately 28.74 meters.