Question

A car moves along a road. While passing through a gas station, the driver sees a house on the right, the visual forms an angle of 39 ° on the direction of the road. Two minutes later he looks back and sees the house: now the angle is 65 °. If the house is 7km from the gas station (in the direction of the road), calculate the speed of the car

Answer 1

Answer:

307.92 km per hour.

Step-by-step explanation:

Let us assume that the distance from the road to the house is x km.

Now, for the case when the house is in front of the car,  

$\tan 39 =\frac{x}{7}$ {Since the distance from the gas station to the house is 7 km.}

⇒ x = 5.668 km.

Now, let us assume that when the driver sees the house to the back then it was y km from the house.

Hence, $\tan 65 =\frac{x}{y} =\frac{5.668}{y}$

⇒ y = 3.264 km.

Therefore, the car moves by ( 7 + 3.264 ) = 10.264 km in 2 minutes {As per given condition}

Therefore, the speed of the car is $\frac{10.264 \times 60}{2}=307.92$ km per hour. (Answer)