Question

From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be30°and45°. Find the distance of the two stones from the foot of the hill. ​

Answer 1

Answer:

Let the distance between the nearer kilometre stone and the hill be 'x' km.

So, the distance between the farther kilometre stone and the hill is '1+x' km since both are on the same side of the hill.

In triangle APB,

tan45

0

=

x

h

⇒1=

x

h

⇒h=x

In triangle AQB,

tan30

0

=

1+x

h

⇒

3

1

=

1+x

h

⇒1+x=

3

h

From equation 1,

1+h=

3

h⇒1=

3

h−h

⇒h=

3

−1

1

⇒h=1.365km

Hence option A is correct.

Answer 2

Answer:

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1.365 Km