A fire in a building B is reported on the telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of $60 °$ to the road and Q observes that it is at an angle of $45 °$ to the road. Which station should send its team and how much will this team have to travel?

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7.36 km

6.32 km

7.32 km

8.32 km

answer is B.

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Detailed Solution

Given that a fire in a building B is reported on the telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of

60 °

to the road and Q observes that it is at an angle of

45 °

to the road.
We have to find the distance between the station and the building.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for can be expressed as

tan θ = opposite adjacent

Suppose P and Q be two fire station 20 Km apart and point B be the building and point A be the fire .Assume AB=h is the height of the building and PB=x is the distance of the fire station P from the building. Then, by using the figure geometry,
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