Question

A road is inclined at an angle of 2 degrees2°. after driving 49004900 feet along this​ road, find the​ driver's increase in altitude.

Answer 1

I think you wrote 4900 twice so will use that as the distance. To solve this it is helpful to draw a picture. The drawing should be of a triangle. Since the driver is driving up at an angle, the 4900 ft will be the hypotenuse of the triangle. since we do not know the values of the other two sides of the triangle we cant solve for the altitude using Pythagorean theorem but we can solve using the sine function on our calculator. As sine of angle is equal to opposite over hypotenuse(sinθ=opposite/hypotenuse). Having θ and the hypotenuse we can solve for opposite or the altitude. using some algebra we get hypotenuse*sinθ=opposite or altitude. now to plug everything in and solve: 4900 ft*(sin(2°))=opposite or altitude=171 ft