# Two roads intersect at 34 degrees. There is one car on each road, and they travel at different speeds of 80km/h and 100km/h. How far apart are the cars after 2 hours? After 2 hours there is a helicopter flying above the 2 cars, the angle of depression is 20 degrees, and the straight line distance is 100km. Determine the altitude of the helicopter.

After 2 hours the fast car A is 200 \ km away, and the slow car B is 160\ km away from the intersection C. The altitude of the helicopter is 34.2\ km.

Two roads intersect at 34^{o}. There are 2 cars traveling on each road at two different speeds of 80 km/hr and 100 km/hr. We have to find out how far apart the 2 cars are after 2 hours. Also given that a helicopter flies above the cars with an angle of depression 20^o and a straight line distance of 100 km, we have to find the altitude of the helicopter.

See the attachment for the figure.

Figure A represents the location of the fast car, and B represents the slow car. C is the intersection of the two roads. H represents the helicopter, assuming that it is flying in the middle of the two cars. h is the altitude of the helicopter.

After 2 hours, the fast car A is 100  km/hr \times 2 hr = 200\ km.

The slow car B is 80 km\hr \times  2 hr = 160\ km , from the intersection C.

This is assuming that here the angle of depression 20^o and the straight line distance100\ km is given to the slow car B. We can find the altitude of the helicopter by considering the right angle triangle  Delta HDB .

sin20^o = \frac{h}{100}

implies h=100 sin 20^o= 34.2\ km .

Therefore the altitude of the helicopter is 34.2\ km .

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