Find the value of X round to the nearest 10th law of cosines.

Image of triangle is missing, so i have attached it.

x = 18

Step-by-step explanation:

From the diagram attached, we can see that the 3 given sides have dimensions of x, 16 and 30.

Also, we see the angle opposite the dimension of x is 30°

Thus,we can use law of cosine to fjnd the value of x. Thus:

x² = 16² + 30² - 2(16 × 30)cos 30

x² = 256 + 900 - (960 × 0.866)

x² = 324.64

x = √324.64

x = 18.02

Approximating to the nearest tenth gives; x = 18

(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