Question

. There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are A and B respectively.

Based on the following figure, answer the questions:

B

60 m

(i) In the given figure, if cos (A + B) = 0 and tan(A-B)= 1 sqrt 3 ;0^ <A+B<90^ ; A > B , then

find the value of A and B.

(ii) Find the width of the river and
height of the other pole.e angles of depressio​

Answer 1

Answer:

Let the width of the river be w.

In ΔABC,

tan 60° =

AB

BC

ABBC

⇒ 3 =

60w

⇒ w =

603=6033=203

In △AED,

tan30° =

AE

ED

AEED

⇒

AE

13=AEw

⇒

AE

13=AE203

⇒ AE = 20

Height of pole CD = AB − AE

= 60 − 20 = 40 m.

Thus, width of river is 203 = 20 x 1.732 = 34.64 m

Height of pole = 40 m.

Answer 2

Answer:

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