MATH SOLVE

5 months ago

Q:
# Find the value of y. Round answer to the nearest tenth if needed

Accepted Solution

A:

Answer:y = 54.1Step-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^21872 = h^2Applying sqr root in both sides:h = 43.27So, 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^21296 + y^2 = g^2Now 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)^21875 + 1296 + y^2 = 24^2 + 48y + y^23171 + y^2 = 576 + 48y + y^2As we have y^2 in both sides we can eliminate them3171 + = 576 + 48yNow subtract 576 in both sides:3171 -576 = 576 + 48y - 5762595 = 48yDivide both sides by 48:2595/48 = 48y/4854.1 = ySo, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:43.3 ^2 + 1296 + 54.2^2 = 6,108.53And the sqrd root of 6,108.53 is approximately 78.1. Verified!!!!So, we can confirm: y = 54.1