Precalc help! i will report any fake answers

D) 41.81 degrees

Step-by-step explanation:

In this problem, we are given a leg length (a=12) and the hypotenuse (c=18).

We need to select which trigonometric identity to use with the acronym SOHCAHTOA:

SOH -> sine=opposite/hypotenuse

CAH -> cosine=adjacent/hypotenuse

TOA -> tangent=opposite/adjacent

Given side a is opposite of angle A and side c is the hypotenuse, we clearly need to use the sine function.

Set up an equation based on the information you have:

sin(A)=12/18

Now take the inverse:

sin^-1(sin(A))=sin^-1(12/18)

A=41.8103149

So the best option is answer D) 41.81 degrees

this answer is !

(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