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

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

the answer would be d

straight away you can eliminate a and c because not all books contain a scientific skill because some may be fiction. c is also wrong because it saids that the only way children can learn is through books which is incorrect.

b is also wrong because reading can be a scientific skill but not always, therefore it is wrong which leaves you with d, the correct answer since it said that it can children learn.

hope this ! : 3

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.