A highway makes an angle of 6 degree with the horizontal Thi

A highway makes an angle of 6 degree with the horizontal. This angle is maintained for a horizontal distance of 5 miles. To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance. A forest ranger spots a fire from a 28-foot tower. The angle of depression from the tower to the fire is 11 degree.

Solution

According to the given question this is a tangent problem. Draw a right angle triangle where the horizontal side is 5 and label the vertical side as x

Now on the opposite side of x the angle is of 6^o and the adjacent side is 5, thats why we use tangent. Now we will solve the problem as follows:

tan(6) = x/5

Multiplying both sides by 5 we get,

5tan(6) = x

x = 0.526 miles

Hence the distance is 0.526 miles.