Answer:
a = 3 ft
Explanation:
The relation between the legs and the hypotenuse of a right-angled triangle can be expressed using the Pythagorean theorem as follows:
[tex] (hypotenuse)^2 = (leg1)^2 + (leg2)^2 [/tex]
In the given triangle, we have:
leg1 = 8 ft and hypotenuse = [tex] \sqrt{73} [/tex] ft
Substitute with the givens in the above equation to get the length of the second leg as follows:
([tex] \sqrt{73} [/tex])² = (8)² + (second leg)²
73 = 64 + (second leg)²
(second leg)² = 9
either second leg = [tex] +\sqrt{9} = 3 ft ............> accepted [/tex]
or second leg = [tex] -\sqrt{9} = -3 ft ................> rejected [/tex] as length cannot be negative
Hope this helps :)
