Find the value of y. round answer to the nearest tenth if needed

y = 54.1

Step-by-step explanation:

The big triangle is divided in two: one on  the left and one on the right. Lets start working with the right one.

We know the right triangle is a right triangle with legs 24 and 36, so we can use Pitagoras to find the hypotenuse (h), in a way that:

24^2 + 36^2 = h^2

1872 = h^2

Applying sqr root in both sides:

h = 43.27

So, the hypotenuse measures 43.27 or 43.3.

Now lets do the same with the triangle of the right which legs are 36 and y, lets find it hypotenuse (g):

36^2 + y^2 = g^2

1296 + y^2 = g^2

Now we will pass to the large triangle, which is composed by the left and the right triangles and has legs of 43.3 and g, and the hypotenuse is 24+y. Lets apply Pitagoras:

43.3^2 + g^2 = (24+y)^2

1875 + 1296 + y^2 = 24^2 + 48y + y^2

3171 + y^2 = 576 + 48y + y^2

As we have y^2 in both sides we can eliminate them

3171 + = 576 + 48y

Now subtract 576 in both sides:

3171 -576 = 576 + 48y - 576

2595 = 48y

Divide both sides by 48:

2595/48 = 48y/48

54.1 = y

So, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:

43.3 ^2 + 1296 + 54.2^2 = 6,108.53

And the sqrd root of 6,108.53 is approximately 78.1. Verified

So, we can confirm: y = 54.1

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