A diagonal of a rectangle is 8cm and forms an angle measuring 30 with one side. Find the area of a rectangle
Let's first draw the picture. The diagonal of your rectangle will be a line that goes from the top left corner of your rectangle to the bottom right corner. This line is the hypotenuse of your RIGHT triangle. The problem tells us that the hypotenuse forms a 30 degree angle with on of the sides. We can pick either side, but I chose to pick the side that includes the left side of the rectangle. Now, we have a 30-60-90 right triangle. The base of the triangle is opposite the 30 degree angle, so it will equal x. The hypotenuse is 2x and the height is x√3.
SO, since we know the hypotenuse is 8cm, we know: 8=2x and x=4; x√3=4√3
The area of a rectangle is b*h, so we multiple 4√3*4 to give us 16√3
Hope that helps!
They're not equivalent.
(vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
(square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as --- it depends on what your textbook/source says).
To solve , you first transform it into the equivalent equation . Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so , thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so , thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
Your answer would be 49.378 meters
Answer:
40
Step-by-step explanation:
you x 8x5