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A boy, who is 5 ft. 6 in. tall, casts a shadow 2 ft long. Find the height of the pole if it casts a shadow 2 yards long.

192 inches

195 inches

198 inches

2 Answers

3 votes
This is a similar triangles problem:

h/s=H/S

In this case:

p/(2yd(36in/yd))=(5(12)+6)/(2ft(12in/ft))

p/72=66/24, now multiply both sides by 72

p=72(66/24)

p=4752/24

p=198 inches
User Richardhsu
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8.4k points
3 votes

Answer:

option C is correct

Height of the pole is, 198 inches

Explanation:

Given: Height of boy = 5ft 6 in , shadow of boy = 2ft

To find the height of pole if it casts a shadow 2 yards long.

Using conversion:

1 yards = 36 inches

1 ft = 12 inches.

Then;

5ft 6 in = 66 inches

2 ft = 24 inches.

2 yards = 72 inches.

Now, using proportions to find the height of pole.

Let height of pole is, h

Proportion says that two ratios are equal.

then;


(height of boy )/(Shadow of boy) = (Height of pole )/(Shadow of pole)

Substitute the values:

height of boy = 66 inches , height of pole = h

Shadow of boy = 24 inches and shadow of pole = 72 inches


(66)/(24) = (h)/(72)

Multiply both sides by 72 we get;


h = (66)/(24) * 72

or


h = 66 * 3 = 198 inches

therefore, the height of the pole is, 198 inches





User Merc
by
8.1k points

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