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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.
Solution
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.
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