Question

The angle of elevation of top of a tower from a point A on the ground is y. On walking 85m towards the tower, the angle of elevation is found to be 2y. If tan 2y =8 / 15, calculate the height of the tower and the distance of tower from A

Answer 1

Answer:

see this attachment...i hope it's help to you

Answer 2

The height of the tower is 40 m

The  distance of tower from A is  160 m

Step-by-step explanation:

from the figure :

$\tan 2y = \frac{8}{15}\\\\\tan 2y = \frac{2\tany }{1-tan^2y }\\\\\frac{8}{15}= \frac{2\tany }{1-tan^2y }\\\\4-4\tan^2y = 15\tan y \\\\4\tan^y + 15\tany-4 =0\\\\4\tan^y+16\tan y-\tan y -4 =0\\\\4\tan y (\tany + 4)-1(\tan y +4)=0\\\\\tan y = \frac{1}{4}\\\\\tan 2y = \frac{h}{x}\\\\\frac{8}{15}= \frac{h}{x}\\\\h = \frac{8x}{15}\\\\\tan y = \frac{h}{x+85}\\\\\frac{1}{4} = \frac{h}{x+85} \\\\\text{solving}\\\\x= 75, h = 40$

hence , The height of the tower is 40 m

The  distance of tower from A is  x+85 = 75 + 85 = 160 m

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