Question

Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. If Jack's and John's eyes are 1.5 meters from the ground and the distance from Jack's eyes to the top of the tower is 50.64 meters, how far is John from the base of the tower? Round your answer to the nearest tenth.


24.5 meters



16.1 meters



22.2 meters



18.8 meters

Answer 1

see the picture attached to better understand the problem

we know that

in the right triangle ABC
cos 40°=AB/AC---> AB=AC*cos 40°---> AB=50.64*cos 40°--> AB=38.79 m
 remember that
AB=BD+DA----> BD=AB-DA
where
BD is the distance of John from the base of the tower
AB=38.79 m  (is the distance of Jack from the base of the tower)
DA=20 m
so
BD=38.79-20----> BD=18.79 m-----> BD=18.8 m

the answer is
18.8 m