Question

A plane rises from take-off andflies at an angle of 15° with thehorizontal runway. When ithas gained 550 feet, find thedistance that the plane hasflown.

Answer 1

Given: The information of a plane flying at angle 15 degree with the runway gaining a height of 550ft

To Determine: The distance flown by the plane

Solution:

The given information, was interpreted in the diagram shown

It can be observed that the information gave a right triangle with a given angle

Note that given a right angle triangle with a reference angle tetha, and sides of the triangle. The side facing the reference angle is the opposite, the side facing the right angle is the hypothenuse, and the other side is the adjacent

So, applying trigonometry ratios, we have

`\begin{gathered} sin\theta=(opposite)/(hypothenuse) \\ cos\theta=(adjacent)/(hypothenuse) \\ tan\theta=(opposite)/(adjacent) \end{gathered}`

From the given diagram,

From the above, opposite and hypothenuse, will get the answer. So

`\begin{gathered} sin15^0=(550)/(c) \\ c* sin15^0=550 \\ c=(550)/(sin15^0) \\ c=(550)/(0.2588) \\ c=2125.04ft \\ c\approx2125ft \end{gathered}`

Hence, the distance traveled is 2125ft to the nearest whole numbe