Question

A policeman is standing near a highway using a radar gun to catch speeders. He aims the gun at a car that has just passed his position and, when the gun is pointing at an angle of 45(degrees) to the direction of the highway, notes that the distance between the car and the gun is increasing at a rate of 100km/h. How fast is the car travelling?

Answer 1

65 km

Answer 2

how?

Answer 3

Happily, 45-deg angle has same "A" and "B" so hypotenuse squared is a squared plus b squared, or 2 a squared. Square root (hypotenuse) is square root (2a squared)
Square root 100 is ten so 10 eq square root (2a squared)

Answer 4

yeah i still don't understand?

Answer 5

think of a big triangle. pointing the radar gun at the car you're looking down the hypotenuse. it's 100 "long" (that's his speed). Because you're looking at a 45-deg angle the distance he's gone down the road is the same as your distance from the road (a trick of trigonometry). Think of the sides of a right triangle. So a^2+b^2=c^2 right? if distance from the road is same as distance he's driven down the road, a=b. so a^2 equals b^2. This makes your equation a^2+b^2=c^2 turn into 2a^2=c^2.Or, c=square root of (2a^2).