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 feet, how far is John from the base of the tower? 24.5 meters 16.1 meters 22.2 meters 18.8 meters

QUESTION POSTED AT 18/04/2020 - 07:04 PM

Answered by admin AT 18/04/2020 - 07:04 PM

tan(40) = (y + 1.5) / (x + 20)

y + 1.5 = (x + 20)[tan(40)]

y = (x + 20)[tan(40)] - 1.5

tan(60) = (y + 1.5) / x

y + 1.5 = (x)[tan(60)]

y = (x)[tan(60)] - 1.5

(x)[tan(60)] - 1.5 = (x + 20)[tan(40)] - 1.5

(x)[tan(60)] = (x + 20)[tan(40)]

(x)[tan(60)] = (x)[tan(40)] + (20)[tan(40)]

(x)[tan(60)] - (x)[tan(40)] = (20)[tan(40)]

(x)[tan(60) - tan(40)] = (20)[tan(40)]

x = [(20)(tan(40))] / [tan(60) - tan(40)]

x = 18.8 meters

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