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radio tower casts a shadow of 8.2 ft long and 836-in 4th grader walking home casts a shadow of 1.5 inches. how tall is the radio tower?

Radio Tower Casts A Shadow Of 82 Ft Long And 836in 4th Grader Walking Home Casts A Shadow Of 15 Inches How Tall Is The Radio Tower class=

Sagot :

Answer

The height of the radio tower is 196.8 ft long

Step-by-step explanation:

Let the height of the radio tower be x

Given that

The base of the radio tower is 8.2ft long

The height of the 4th grader = 36 ft long

The base of the 4th grader = 1.5 ft long

To find the value of x

Since the figures are similar

We will be applying the triangle similarity theorem

Let assume the height of the radio tower is AB

The base of the radio tower is BC

Also, let the height of the 4th grader be XY

Let the base of the 4th grader be YZ

This implies that

AB = x

BC = 8.2

XY = 36

YZ = 1.5

Applying the triangle similarity theorem

We will have

AB / XY = BC / YZ

x / 36 = 8.2 / 1.5

Cross multiply

x * 1.5 = 8.2 * 36

1.5x =295.2

Divide both sides by 1.5

1.5x/1.5 = 295.2/1.5

x = 295.2 / 1.5

x = 196.8 ft long

Hence, the height of the radio tower is 196.8 ft long

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