Question

FLAGPOLE Julie is 6 feet tall. If she stands 15 feet from the flagpole and holds a cardboard square, the edges of the square line up with the top and bottom of the flagpole. Approximate the height of the flagpole

Answer 1

44 ft

Explanation:

Given: Julie is 6 feet tall

She stands 15 feet from the flagpole.

The edges of the square line up with the top and bottom of the flagpole.

Lets assume the height of flagpole be "h".

As given, the edges of the square line up with the top and bottom of the flagpole.

∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.

Now, finding the height of flagpole by using tangent rule.

we know,
`tan\theta= (Opposite)/(adjacent)`

Remember, both the angle are equal.

∴ Ratio of opposite and adjacent leg for both right angle triangle=
`(6)/(15) : (h-6)/(15)`

We can put it;
`(6)/(15) = (15)/(h-6)`

Solving the equation now

⇒
`(6)/(15) = (15)/(h-6)`

Multiplying both side by 15

⇒
`6 = (15* 15)/(h-6)`

Multiplying both side by (h-6)

⇒
`6* (h-6) = 15* 15`

Distributive property of multiplication

⇒
`6h-36= 225`

Adding both side by 36

⇒
`6h= 225+36`

Dividing both side by 6

⇒
`h= (261)/(6)`

∴
`h= 43.5\ feet`
`\approx 44 feet`

Hence, the height of flagpole is 44 feet.