The length of the hypotenuse of the triangle is 67.5 inches.
5)The image shows a right triangle with one angle measuring 30 degrees and one side measuring 5 inches. We are asked to solve for the length of the hypotenuse, which is labeled as $66+x$.
To solve this problem, we can use the trigonometric function sine. Sine is defined as the opposite side over the hypotenuse. In this case, the opposite side is 5 inches and the hypotenuse is $66+x$ inches. Therefore, we have the following equation:
sin(30°) = 5 / (66+x)
We can solve for $x$ by multiplying both sides of the equation by $66+x$ and then subtracting 5 from both sides. This gives us the following equation:
66+x = 5 sin(30°) + 5
Subtracting 66 from both sides and then dividing both sides by 1 gives us the following solution for $x$:
x = 5 sin(30°) - 1
Using a calculator, we can find that sin(30°) = 0.5. Therefore, the solution for $x$ is:
x = 5 * 0.5 - 1
x = 1.5