Answer:
311.41 degrees
Step-by-step explanation:
If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).
Let's assume we're in Quadrant IV. Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.
According to the Pythagorean Theorem, (-3)^2 + x^2 = 4^2, or,
x^2 = 16 - 9 = 7.
Then x is either √7 or -√7.
To find the angle Ф, use the inverse sine function:
Ф = arcsin (-3/4). Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees. We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."
Circumference/diameter= 47.1/15=3.14
Answer:
The answer to your question is 23.42 ft
Step-by-step explanation:
Data
base = 6 ft
height = 4 ft
Process
1.- Calculate the length of the rectangle. Only consider the base and the left and right sides.
Length = 6 + 4 + 4
Length = 14 ft
2.- Calculate the Perimeter of the semicircle
Formula
Perimeter = 2πr/2 = πr
-Calculate the radius
radius = 6/2 = 3 ft
-Find the perimeter
Perimeter = 2(3.14)(3)/2
-Result
Perimeter = 9.42 ft
3.- Calculate the perimeter of the window
Perimeter = 14 + 9.42
= 23.42 ft
