Question

a kite is flying 16 ft off the ground. it’s line is pulled taut and casts a 12 ft shadow. find the length of the line. if necessary, round to the nearest tenth

Answer 1

We are given the following triangle

where we want to solve for x. Note that this triangle is a right triangle. Therefore, the missing side is the hypotenuse of the triangle.

To find the measure of the hypotenuse, we are going to use pythagora's theorem, which states

Given the triangle

we have the equation

$c^2=a^2+b^2$

in our case, we have x=c, a=12, b=16. So we have the equation

$x^2=12^2+16^2=144+256=400$

So, if we apply the square root on both sides, we get

$x=\sqrt[2]{400}=\pm20$

however, as x is a distance, it must be a positive number. So we have that

$x=20$