Question

What are two different ways you could find the value of a? Explain these methods. 16

Answer 1

The image is in the attachments

Answer: a = 20

Step-by-step explanation: You could find the value of a by using the Pythagorean Theorem, which states that:

hypotenuse² = side² + side²

In the first method, we use the whole triangle, i.e., without the line separating it in 2, we have a right triangle with measures:

side = 15

side = a

hypotenuse = 9+16 = 25

then:

25² = a² + 15²

a = $\sqrt{25^{2} - 15^{2} }$

a = 20

The second method would be using the two right triangles:

with measures hypotenuse = 15 and side = 9, from the left triangle, we found the side that is commom to both triangles:

15² = 9² + x²

x = $\sqrt{15^{2} - 9^{2} }$

x = 12

With x, find a:

a² = 12² + 16²

a = $\sqrt{144 + 256}$

a = 20