Question

If the angle of depression of a boat from a 12 m
high bridge is 60°, then find the distance of the
boat from the base of the bridge.​

Answer 1

Step-by-step explanation:

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Answer 2

The distance from the bottom of the bridge to the boat is 4√3m

Given

• 12 m
• high bridge
• angle of depression 60°

To find

• distance of the
• boat from the base of the bridge.

solution

we are provided with the height of the bridge and angle of depression of the boat and are asked to find the distance from the bottom of the bridge to that of boat.

kindly refer the attachment for the figure in this case

The question could be answered by using trigonometric functions involved with the situation of the question which would be understandable from the figure.

Let the triangle ABC be a right triangle and the height be represented by AC which is 12 m.

now the required length is AB.

the angle ACB is 30 degrees which could be estimated from the anger of depression that is 60 degrees as provided from the question. ( Shown in figure)

now,

considering the right triangle ABC,

tan30 = AB/AC

or, AB = tan30 × AC

or, AB = 1/√3 × 12 ( from given values)

or, AB = 12√3/3

or, AB = 4√3m

therefore, the distance from the bottom of the bridge to the boat is 4√3m

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