MEASURING LENGTHS BASED ON THE ANGLE OF INCLINATION/DECLINATION; APPLYING THE LAWS OF SINES AND/OR COSINES; FINDING THE TRIGONOMETRIC VALUE USING THE SUM/DIFFERENCE FORMULA.

Question

Question

(1): Suppose that a person is on top of a building and the person is 1025 feet above the ground. The person throws an object in a downward diagonal direction. The person who threw the object is looking down on the object at an angle of 30 degrees.

(a)   What is the distance between the person, who is on top of the building, and the object lying on the ground?

(b)  How many feet apart is the object from the building?

Answer 1

side b=1025'

If the ball is on the ground forming a 30° angle to the person/building; you want side c. So α=30°.

a/sinα=b/sinβ=c

1025/.866=1183.567...'

Now you want side a.

Answer 2

The length of the side opposite the 30° is one-half the length of the hypotenuse.

1025 = (0.5)(d)

2050 = d