Question

A small radio transmitter broadcasts in a 44 mile radius. If you drive along a straight line from a city 60 miles north of the transmitter to a second city 59 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

Answer: 87.03

Step-by-step explanation:

The outer parts (2) of the secant line containing α and β refers to the distance travelled where there is no signal. The middle part is where there is signal presence. To get the altitude of the triangle:

Hc= 2(A/c)

To find the area;

A= 1/2(59)(60)

A= 1770

Use Pythagoras theorem to get c:

C= =√(60)^2+(59)^2

=√7081

Hc=2(1770/√7081)

   =3540√7081/7081

Solve for x using Pythagoras theorem:

x= (√44^2-Hc^2) + (√44^2-Hc^2)

where Hc= 3540√7081/7081

      =87.03