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:
$\frac{sin(32)}{800} = \frac{sin(90)}{AC}$
$AC=1509.66$

Lastly, we need to utilize the sine law again to find the length of segment CD or the width of the field:
$\frac{sin(27)}{1509.66} = \frac{sin(5)}{CD}$
$CD=290$

ANSWER: The width of the field is 290 ft.