Question

Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long. If the hook is 5 meters from the flagpole, how tall is the flagpole?

Answer 1

The flagpole 12 meters tall

Explanation:

Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long

∵ The hook is 5 meters from the flag pole

∵ The flagpole and the ground ⊥ to each other

By using Pythagoras theorem:

hypothenus side is 13m

base is 5m

how tall is the flagpole is x

`13^2=x^2+5^2\\\\169=x^2+25\\\\x^2=169-25\\\\x^2=144\\\\x=12m`

The flagpole 12 meters tall

Answer 2

12 meters

Explanation:

Looking at the problem we can see that it typifies a right angled triangle. The rope running from the top of the flagpole to the hook on the ground is the hypotenuse of the triangle. Let us call this hypotenuse c. Let the distance between the hook and the foot of the flagpole be b. Let the height of the flagpole be a.

From Pythagoras theorem;

c^2 = a^2 + b^2

a^2= c^2 - b^2

a= √c^2-b^2

From the question

c= 13 metres

b= 5 metres

a= the unknown

a= √c^2-b^2

a= √(13)^2 - (5)^2

a= √169 - 25

a= √144

a= 12 meters