ehaynie
29.02.2020 •
Mathematics
David wants to measure the width of a road
he chooses two points, A and B, 40m apart.
The angles made with a lamppost, P, on the opposite side are measured.
Angle BAP=45 degrees
Angle ABP=60 degrees
Work out the width, in metres, of the road. give your answer correct to 3 significant figures
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Ответ:
The width of the road = 25.359 m
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
So, The width of the road = 25.359 m
Ответ:
Step-by-step explanation:
13) Second angle (side shared)
14) Second side (one side shared)
15) Second side (angles where they meet are equal)
16) Second angle (one angle equal cause of a rule)
17) Third side
18) Second side