# math

posted by darian

a flagpole is 25 feet tall. a truck runs into the pole and bends it at the very bottom of the pole but the rest of the pole remains straight. after the accident we measure the angle of elevation to the top of the pole from a point 30 feet from the base of the pole in the same direction as the pole bends. the angle of elevation is 45 degrees. what is the distance between where the top of the pole used to be and where it ended up?

1. Steve

If the top of the pole moved from P to Q, and the base of the pole is at A, and the observation point is at B,

sinQ/30 = sin45/25
sinQ = 0.848
Q = 58°

Now you have two angles of triangle ABQ, so you know angle θ=QAB.

PQ^2 = 25^2 + 25^2 - 2(25)(25)cos(90-θ)
= 1250 - 1250sinθ
= 1250(1-sin(pi-(45+Q))
= 1250(1-sin(45°+58°))
= 32
PQ = √32 = 5.66

## Similar Questions

1. ### Precalculus

A woman standing on a hill sees a flagpole that she knows to be 60 ft tall. the angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. find her horizontal distance …
2. ### Precalculus

A woman standing on a hill sees a flagpole that she knows to be 60 ft tall. the angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. find her horizontal distance …
3. ### trig

A woman standing on a hill sees a flagpole that she knows is 65 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. Find her distance x from the pole. (Round …
4. ### Math

At a distance of 56 feet from the base of a flag pole, the angle of elevationi to the top of a flag that is 3.1 feet tall is 25.6 degrees. the angle of elevation to the bottom of the flag is 22.9 degrees. the pole extends 1 foot above …
5. ### another math

At a distance of 34 feet from the base of a flag pole, the angle of elevation to the top of a flag is 48.6°. The flag itself is 5.1 feet tall. The angle of elevation to the bottom of the flag is 44.6°. The pole extends 1 foot above …
6. ### Trigonometric

A woman standing on a hill sees a flagpole that she knows is 55 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. Find her distance x from the pole.
7. ### Math

1. To find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit 8 feet tall, measure the angle of elevation to the top of the pole to be 36*. to the nearest foot, what is the height …
8. ### Geometry

What is the height of a pole standing 20 feet from the base of pole and measure the angle of the elevation to the top of the pole to be 54 degrees what's the height of the pole
9. ### maths

from a point P on a level ground and directly west of a pole,the angle of elevation from the top of the pole is 045 and from point Q east of the pole the angle of elevation of the pole the angle of elevation of the top of the pole …
10. ### math

A street light is at the top of a 11 ft. tall pole. A man 6.2 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 31 feet from the pole?

More Similar Questions