Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an angle.

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse =

Now, using the sine ratio for the angle, we have

Therefore, the value of is .

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

(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