Question

A drone is flying over a college campus. the drone spots the cafeteria on the west end of campus at a 27 degree angle of depression and the sports complex on the east end of campus at a 34 degree angle of depression. If the cafeteria and sports complex are sped aged by a straight road 2.3 miles long how high is the drone please help I don’t get this

Answer 1

Answer:

0.67 miles

Step-by-step explanation:

in the attached diagram, the drone is at B. The cafeteria is at A and the sport complex at C. We want to determine how high up the drone is, i.e. |BMM

Using Trigonometry:

In Right Triangle ABM

$Tan 27^\circ=\frac{h}{y} \\h=yTan 27^\circ$

Similarly, in Right Triangle BMC

$Tan 34^\circ=\frac{h}{2.3-y} \\h=(2.3-y)Tan 34^\circ$

Therefore:

$h=yTan 27^\circ =(2.3-y)Tan 34^\circ\\yTan 27^\circ =(2.3-y)Tan 34^\circ\\yTan 27^\circ =2.3Tan 34^\circ-yTan 34^\circ\\yTan 27^\circ +yTan 34^\circ=2.3Tan 34^\circ\\y(Tan 27^\circ+Tan 34^\circ)=2.3Tan 34^\circ\\y=\dfrac{2.3Tan 34^\circ}{Tan 27^\circ+Tan 34^\circ} \\y=1.3102$

Since h=yTan 27^\circ

h=1.3102Tan 27^\circ

h=0.6676 miles

The height of the drone therefore is 0.67 miles (correct to 2 decimal places)