Question

A flag pole is 12 ft high in the air. The Distance from the top of the pole to a point on the ground where Janae is standing is 15ft. How far is she standing from the bottom of the pole?

Answer 1

Janae is standing at a distance of 9 feet from the bottom of pole

Solution:

The flag pole, and the point where Janae is standing and the ground forms a right angled triangle

The figure is attached below

ABC is a right angled triangle

AB is the height of pole

AB = 12 feet

C is the point where Janae is standing

AC is the distance from the top of the pole to a point on the ground where Janae is standing

AC = 15 feet

BC is the distance between bottom of pole and the point on the ground where Janae is standing

We have to find BC

We can use pythagoras theorem for right angled triangle

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition for right angled angle triangle ABC,

`AC^2 = AB^2+BC^2`

Substituting the values we get,

`15^2=12^2+BC^2\\\\225 = 144 + BC^2\\\\BC^2 = 225-144\\\\BC^2=81\\\\\text{Taking square root on both sides }\\\\BC = 9`

Thus she is standing at a distance of 9 feet from the bottom of pole