Which represents the reference angle for 3pi/4?
1 answer:
You might be interested in
Question 1:
This is a 45-45-90 right triangle. If the leg length is
, then the hypotenuse length will be 
.
The leg length of this 45-45-90 right triangle is 8. Multiply that with the square root of 2. You get
. Thus, the last choice is your answer.
Question 2:
This triangle can be identified as a 30-60-90 right triangle.
Let's say the smallest leg as a length of.
Then, the longer leg will have a length of
.
Also, the hypotenuse will have a length of
This triangle follows this format, making it a 30-60-90 right triangle. Thus, the angles are 30, 60, and 90.
Hope this helps! :)
This is a 45-45-90 right triangle. If the leg length is
The leg length of this 45-45-90 right triangle is 8. Multiply that with the square root of 2. You get
Question 2:
This triangle can be identified as a 30-60-90 right triangle.
Let's say the smallest leg as a length of
Then, the longer leg will have a length of
Also, the hypotenuse will have a length of
This triangle follows this format, making it a 30-60-90 right triangle. Thus, the angles are 30, 60, and 90.
Hope this helps! :)
Let's carry this math sentence over to its natural, "shapey" element. We're going to look at each term not as an ordinary number, but as <em>the area of some shape</em>.
x² (read as "x <em>squared"</em>) can be seen as the area of a square with side lengths of x. 2x can similarly be seen as the area of a <em>rectangle </em>with a length of x and a width of 2. (Picture 1)
What's our question actually asking, though? Something about <em>perfect squares</em>. More specifically, we're looking for something to add on that'll <em>make this thing a perfect square</em>. We're trying to find a missing piece we can slot in to make a square, in other words. Problem is, our shapes don't look much like a square if we put them together right now. We need to do a little cutting and gluing first.
First, we're gonna cut the 2x rectangle lengthwise, getting two rectangles with an area of x, a length of 1, and a width of x. Next, we're going to attach them to the x² square, creating this shape that looks, strangely, like a square with a little bit missing from it (picture 2). What we're trying to do is <em>complete this square, </em>to find the area of that little missing chunk.
As it turns out, we have all the information we need for this. Notice that, using the lengths of the x rectangles, we can find that the square's dimensions are 1 x 1, which means that its area is 1 x 1 = 1.
If we tack this new area on to our original expression, we've "completed the square!" We now have a perfect square with side lengths of (x + 1) and an area of (x + 1)² (picture 3).
So, our final expression is x² + 2x + 1, and the missing constant - the area of the "missing square" we had to find to complete our larger one - is 1.
