Answer :
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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 = [tex]\sqrt{25^{2} - 15^{2} }[/tex]
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 = [tex]\sqrt{15^{2} - 9^{2} }[/tex]
x = 12
With x, find a:
a² = 12² + 16²
a = [tex]\sqrt{144 + 256}[/tex]
a = 20
