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..??​

Answer 1

Answer:

Let AB be hill of which B is foot of hill and D and C are two consecutive km stones.

∴ DC = 1 km = 1000 m

In right angled △ABC, tan 45˚ = AB/BC

1 = h/x

x = h …..(i)

In right angled △ABD, tan 30˚ = AB/BD

1/√3 = h/(x + 1000)

x + 1000 = h√3 ……(ii)

But from equation (i), x = h,

∴ x + 1000 = x√3

x(√3 – 1) = 1000

x = 1000/(√3 – 1) × (√3 + 1)/( √3 + 1)

= 1000(√3 + 1)/2

= 500(√3 + 1)

= 500 × 2.732

= 1366 metre

= 1.366 km

∴ Ist km stone is 1.366 km and IInd km stone is 2.366 km from foot of hill.

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Answer 2

☆☆ 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..?? ☆☆

Answer - {in the attachment}

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