Question

Will FAN and MEDAL

A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.




a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.

Answer 1

the complete question in the attached figure

Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.

in the triangle ACD
sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1

in the triangle BCD
sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2

equation 1=equation 2
sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD
sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]
BD=15979 ft

in the triangle BCD
cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491
BC=17491 ft

the answer part 1) BC is 17491 ft

Part 2) Find CD, the height of the plane from the ground, to the nearest foot.

CD=sin24*BD ( remember equation 2)
BD=15979 ft
CD=sin24*15979 -----------> CD=6499 ft

the answer part 2) CD is 6499 ft