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Q.

A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is $45 °$ . Which of the following statements is correct?

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a

Breadth of the river is twice the height of the tower.

b

Breadth of the river is equal to the height of the tower.

c

Breadth of the river is half of the height of the tower.

d

None of the above.

answer is C.

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Detailed Solution

It is given that; the angle of elevation of the top of a tower on the opposite side bank is

45 °

. Suppose, the height of the tower be h and the breadth of the river be x.
We have to find the relation between the breadth of the river and the height of the tower.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for tan for

45 °

angle is

tan 45 ° = 1

.
Then, by using the figure geometry,
Question Image

Question Image

tan 45 ° = h x ⇒ 1 = h x ⇒ h = x

Thus, the breadth of the river is equal to the height of the tower.
Therefore, option 3 is correct.

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