Question

The sun casts a shadow from a flag pole. The height of the flag pole is three time the lenght of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the height of the flag pole

Answer 1

The height of the flag pole =
`6√(10) feet`

Explanation:

Let us consider, the length of the shadow = x

According to the question,

The length of the flag pole = 3 times length of the shadow.

= 3x

From the figure, By "Pythagoras theorem",

`x^(2) + (3x)^(2) = 20^(2)\\`

`x^(2) + 9x^(2) = 400`

`10x^(2) = 400\\ x^(2) = 40\\ x = √(40) \\ x = 2√(10)`

So, The length of flag pole =
`3* x`

=
`3*2√(10) = 6√(10) feet`

Answer 2

The height of the flag pole will be = 18.96 ft.

Explanation:

See the attached diagram.

AB is the flag pole and the length of the shadow is AC.

Now, Δ ABC is a right triangle and has AB = 3x ft., BC = 20 ft. and AC = x ft.

So, applying Pythagoras theorem ,

AB² + AC² = BC²

⇒ (3x)² + x² = 20²

⇒ 10x² = 400

⇒ x² = 40

⇒ x = 6.32 ft. (Approx.)

So, the height of the flag pole will be = 3x = 3 × 6.32 = 18.96 ft. (Answer)