Question

As a part of their weather unit, Anoki’s science class took a hot air balloon ride. As they passed over a fenced field, the angle of depression of the closer side of the fence was 32°, and the angle of depression of the farther side of the fence was 27°. If the height of the balloon was 800 feet, estimate the width of the field. Round your answer to the nearest foot. 2016_01_25_17_23_501.png The width of the field is about feet

Answer 1

Please refer to the figure attached for the diagram of this problem.

Steps needed to find the width of the field (CD):

First, we should note that angle d would be equal to 27 degrees because there are two parallel lines that are cut by a transversal. Furthermore, angle a would be equal to 5 degrees since we just need to subtract 27 from 32.

We then subtract 27 and 5 from 180 to get angle c.
`180-27-5=148`. Angle c is therefore 148 degrees.

Next, we need to find angle e which is just the supplementary of angle c. Angle e therefore measures
`180-148=32` degrees.

For the next step we use sine law to find the length of segment AC:

`(sin(32))/(800) = (sin(90))/(AC)`

`AC=1509.66`

Lastly, we need to utilize the sine law again to find the length of segment CD or the width of the field:

`(sin(27))/(1509.66) = (sin(5))/(CD)`

`CD=290`

ANSWER: The width of the field is 290 ft.