Kite string 53 degrees 300 feet.

Question

You are holding a kite string in your hands. The angle of elevation from your hand to the kite is 53 degrees and the distance to the kite is 300 feet. Your hand is 4 feet above the ground. How high is the kite?

 

Please tell me how to do this step by step.

Answer 1

We can draw a right triangle.

We have a 53 degree angle up from the hand to the kite

giving a hypotenuse of 300 ft in length from hand to kite.

Going vertically down from kite to ground we create a

right triangle.

 

               * kite

              /|

            /  |

          /    |

        /      | H-4

300 /       |

    /_____|

   *

  hand

 

REMEMBER:  WHEN YOU SOLVE FOR HEIGHT H,

ADD 4 FT BECAUSE THE HAND IS 4 FT ABOVE GROUND.

That is why I put H-4 on the opposite leg across from

our 53 degree angle.

 

We can use the sine function... sin a = opposite/hypotenuse

 

sin 53 = (H-4)/300

H-4 = 300(sin 53)

H = 300(sin 53) + 4

H = 243.6 ft

 

The kite is approximately 243.6 ft above the ground

Answer 2

1. your hand is 4' from the ground, and the kite is 300' from your hand, which means the kite is 304' from the ground.

 

2. the ground is a straight line to your right, and it intersects with a perpendicular line which reaches the kite.

 

3. the distance to the kite is a slanted line which forms a right triangle, and that distance is the hypotenuse of the triangle

 

4. the angle of the hypotenuse and the ground 53^o

 

5. the sine of an angle is the side opposite the angle divided by the hypotenuse

 

6. our equation becomes sine 53^o = opposite/hypotenuse = opp/304'

 

7. the sine of 53^o is 0.7986, so our equation becomes

0.7986 = opp/304'

 

8. solving, opp ≅ 242.8'