From the top of hill the angle of depression

Asked by admin @ 23/08/2021 in Math viewed by 251 People

From the top of hill the angle of depression of two consecutive Kallu kilometre stone due to East are found to be 30 degree

and 45 degree find the height of the hill

Answered by admin @ 23/08/2021

1.366 km

Explanation:

Let AB is the height of the hill and two stones are C and D respectively where depression is 45 degree and 30 degree. The distance between C and D is 1 km.

Here depression and hill has formed right angle triangles with the base. We have to find the height of the hill with this through trigonometry.

In triangle ABC, tan 45 = height/base = AB/BC
or, 1 = AB/BC [ As tan 45 degree = 1]
or, AB = BC ..........(i)

Again, triangle ABD, tan 30 = AB/BD
or, 1√3=ABBC+CD [tan 30 = 1√3 =1/1.732]
or, 11.732=ABAB+1 [ As AB = BC from (i) above]

or, 1.732 AB = AB +1

or, 1.732 AB - AB = 1

or, AB(1.732-1) = 1

or, AB * 0.732 = 1

or AB = 1/0.732 = 1.366

Hence height of the hill 1.366 km

Take any three non-collinear points a b c and draw triangle a,b,c. through each vertex of the triangle draw a line parallel to the opposite side using ruler and compass

Asked by wiki @ 15/11/2022 in Mathematics viewed by 1496 persons

From the top of hill the angle of depression

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