Answer:
x = 12.1532°
General Formulas and Concepts:
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] sinθ = opposite over hypotenuse
- Inverse Trig
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
Angle θ = <em>x</em>
Opposite Leg = 4
Hypotenuse = 19
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [sine]: sinx = 4/19
- Inverse trig: x = sin⁻¹(4/19)
- Evaluate: x = 12.1532°
I constructed the figure with the information that you provide, please check the picture.
Since there is a right triangle inside the parallelogram, the parallelogram is a rectangle with

and

; remember that the area of a rectangle is (length)(width), so we can substitute our values to find its area:


On the other hand, the triangle attached to the top of the parallelogram has

, and

; since the area of a triangle is

, we can substitute our values to get:


Now the only thing lefts is add the area of the parallelogram and the triangle to get our total area:

We can conclude that the area of the figure is

.
The Perimeter of a Rectangle.
It's the sum of all its sides.
L + W + L + W or 2(L + W)