Question

From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 45° and 30° respectively. Find the height of the hill.(please brief why the distance between the stones is taken as 1)

Answer 1

Answer: 1.366 km

Step-by-step explanation:

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, 1.732 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

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Answer 2

Answer:

The answer is in hand written form

Step-by-step explanation:

The distance between the stones is taken as 1 bcoz consecutive means the next one

For ex:

You travelled 2 km so the consecutive km is 3

that is you should add 1 with previous number