The classic 60° triangle has a hypotenuse of length 2, an opposite side of length √3 and an adjacent side of length the value of cos(60°)

Using the trigonometry rule for the cosine, we will see that:

cos(60°) = 1/2

Remember that in a right triangle, we have that:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Here we have:

Replacing all that in the equation we get:

cos(60°) = 1/2

If you want to learn more, you can read:

link

The trigonometric values for cos are C = A/H, which means that to find cos(60), you need to divide the adjacent side by the hypotenuse, which in this case gives you 1/2, so that is the value of cos(60).

I hope this helps!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240