Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 months ago

# math help?

A pole that is 2.9m tall casts a shadow that is 1.53m long. At the same time, a nearby tower casts a shadow that is

45.25m long. How tall is the tower? Round your answer to the nearest meter.

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• They are similar triangles, so there is a direct ratio between them

A pole that is 2.9m tall casts a shadow that is 1.53m long.

2.9/1.53 = 1.9

At the same time, a nearby tower casts a shadow that is 45.25m long

h/45.25 = 1.9

h = 1.9 x 45.25

h = 85.77

Height of tower = 86 metres

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• The height of the tower works out as 86 meters rounded up.

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• A pole that is 2.9 m tall casts a shadow that is 1.53 m long.

At the same time, a nearby tower casts a shadow that is 45.25 m long.

t/45.25 = 2.9/1.53

t ≈ 85.768

The tower is 86 meters tall

(Answer rounded to the nearest meter).

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• 2.9*45.25/1.53 =

85.77 m

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• The ratio of height to shadow length is the same for the pole and tower.

x/45.25 = 2.9/1.53

x ≅ 85.76 m

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• // Set up a proportion comparing heights to shadows,

// with x representing the height of the tower.

// Then solve for x.

2.9 cm........x

--------- = ---------

1.53m.....45.25m

......(29 cm)(45.25m)

x = ----------------------

..............1.53m

x = 857.68cm = 8.58m = 9m (rounded to the nearest meter)......ANS

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• Hint:

They have the same ratio

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• By ratios we have 2.9/1.53 = x/45.25; so that x = 45.25*(2.9/1.53) = 85.76797386 meters, you can do the rounding. ANS.

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• 2.9/1.53 = 1.89

Pole is 1.89 times taller than its shadow

45.25 x 1.89 = 85.52 meters rounded up to 86 meters

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