Question

Two-person standing on the same side of a tower in a straight line with it measures the angle of elevation of the top of the tower as 25° and 50° respectively. If the height of the tower is 70 m find the distance between the two-person.

Answer 1

Let CD be the distance between the two persons.
In ΔABC,

cot 50° = `"BC"/"AB"`

cot (90° - 40°) = `"BC"/70`

BC = 70 tan 40°

BC = 70 x 0.8391 = 58.74 m

In ΔABD,

cot 25° = `"BD"/"AB"`

cot (90° - 65°) = `"BD"/70`

tan 65° = `"BD"/70`

BD = 70 tan 65°

BD = 70 x 2.11451 = 150.12 m

CD = 150.12 - 58.74 = 91.38 m

∴ The distance between the two person be 91.38 m.