Hello, nathan02079!

Streelights A, B, C, D, and E are placed 50 m apart on the main road.

The light from a streetlight is effective up to a distance of 60 m.

(a) Find the distance from A to the farthest point on the side road that is illuminated.

(b) Determine the length of the side road that is illuminated by both lights C and D. Code:

F *
o
* \
* \
* \
* 21° \
o--------o--------o--------o-------o
A 50 B 50 C 50 D 50 E

From , draw perpendicular to the side road.

In right triangle m.

Hence, streetlight does *not* effectively illuminate the side road.

Code:

G *
o
* /
* /
* / 60
* 21° /
o-------o-------o--------o
A 50 B 50 C 50 D

Draw so that is obtuse.

Law of Sines: .

. . Then: .

Law of Sines: . .(a)