Answer:
<u>The width of the road = 25.359 m</u>
Step-by-step explanation:
See the attached figure which represents the problem.
The length of AB = 40 m
let the width of the road w.
Construct PC perpendicular to AB, So, the measure of angle C = 90°
∠B = 60° and ∠A = 45°
Let the length of AC = x, so, the length of BC = 40-x
At ΔBCP which is a right triangle at C
tan B = opposite/adjacent = w/(40-x)
w = (40-x) * tan B ⇒(1)
At ΔACP which is a right triangle at C
tan A = opposite/adjacent = w/x
w = x * tan A ⇒(2)
from (1) and (2)
(40-x) * tan B = x * tan A
40 tan B - x *tan B = x tan A
40 tan B = x tan A + x *tan B
40 tan B = x (tan A + tan B)
x = (40 tan B)/(tan A + tan B) = (40 tan 60)/(tan 60 + tan 45) = 25.359 m
substitute at (2) with x
w = x tan A = 25.359 tan 45 = 25.359 m
<u>So, The width of the road = 25.359 m</u>
