Question

Charlie is watching hot air balloons. Balloon A has risen at a 60° angle. Balloon B has risen at an 82° angle. If the distance from balloon A to the ground is 1,400 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number.
Two points labeled Balloon A and Balloon B are connected to a point labeled Charlie, which is on a straight line labeled Ground. A dashed line connects point Balloon A to line Ground; another dashed line connects point Balloon B to line Ground; both dashed lines form a right angle with line Ground; the angle formed from point Balloon A, point Charlie, and line Ground measures x degrees; and the angle formed by point Balloon B, point Charlie, and line Ground measures y degrees.


999 feet

1,005 feet

1,052 feet

1,102 feet

Answer 1

Answer:

(B)1005 feet

Step-by-step explanation:

In the attached diagram

$\angle y =82^\circ\\\angle x =60^\circ$

|AG|=1400 feet

Distance from point C to point G=|CG|

Using Trigonometry in Triangle ACG

$\tan 60^\circ=\dfrac{1400}{CG}\\ CG=\dfrac{1400}{\tan 60^\circ}\\\approx 808 feet$

Using Trigonometry in Triangle BCG'

$\tan 82^\circ=\dfrac{1400}{CG'}\\ CG'=\dfrac{1400}{\tan 82^\circ}\\\approx 197 feet$

Therefore, the distance from balloon B from balloon A

=CG+CG'

=808+197

=1005 feet