Question

Find the exact value of y.

Answer 1

Answer:

$y = 2\sqrt{10}$

Step-by-step explanation:

In left small right triangle: we have the square of left side = 5^2 + y^2 = 25 + y^2

In right small right triangle: we have the square of right side = 8^2 + y^2 = 64 + y^2

In the large right triangle, we have (25 + y^2) + (64 + y^2) = (5 + 8)^2

89 + 2y^2 = 13^2 = 169

2y^2 = 169 - 89 = 80

y = 80/2 = 40

so

$y=\sqrt{40} = 2\sqrt{10}$