While cruising at a steady speed of 400 km/h, you identify a storm cloud straight ahead 45 km away. To avoid turbulence, you start climbing at an angle of elevation of 15°. If you maintain this speed and direction for 6 min, how far will you be from the storm

Question

Mathematics

Maestro

19 September, 15:36

While cruising at a steady speed of 400 km/h, you identify a storm cloud straight ahead 45 km away. To avoid turbulence, you start climbing at an angle of elevation of 15°. If you maintain this speed and direction for 6 min, how far will you be from the storm

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Aguilar · Answer 1

First calculate distance traveled after 6 min.

400 * (6/60) = 400 * (1/10) = 40 km

Next, draw triangle with 2 sides being 45 and 40. The included angle between these sides is 15, the angle of elevation. The third side is distance from plane to storm cloud.

Next, use Law of cosines to find distance.

d = sqrt (40^2 + 45^2 - 2 (40) (45) cos (15))

d = 12.152 km