Question 254711: Special Right Triangles:
45-45-90 Triangle and the 60-30-90. Can you explain to me how to do it B/c I'm Lost On that part. Can you take it step by step. My teacher cannot teach and I'm in need of help. On this specific part. Send me a few examples. I have a quiz tomorrow so I need this asap.
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! We have 2 special triangles; (1) 45-45-90 and (2) 30 - 60-90. These refer to degree measures in a triangle. You may remember that all degrees must add up to 180.
(1) 45-45-90.
Notice 2 numbers are the same That means that 2 sides or legs are the same.
Suppose we call them x and x. We can use Pythagorean theorem to get the hypotenuse as
where a and be are the legs and a = x and b = x. We get
now x^2 + x^2 are like terms and become 2x^2 as
To solve for c, we take a sqrt to get
So, the 45- 45- 90 triangle can be expressed as x -x - xsqrt(2).
We can easily remember this: How many equal angles are there? 2 what kind of a root do I use? 2.It is like we are gluing sqrt(2) onto the side number.
--
EX:
a = 3, b = 3, c = ?
using the relationship, we just take the side and glue a sqrt(2) onto it for the hypotenuse. I call this going forward" because you are going forward from the leg to hypotenuse. Going forward means "multiply" So, c = 3sqrt(2)
--
EX:
a = 18, b = 18, c = ?
using the relationship, we just take the side and glue a sqrt(2) onto it for the hypotenuse. I call this going forward" because you are going forward from the leg to hypotenuse. Going forward means "multiply" So c = 18sqrt(2).
--
EX:
a = ?, b = ?, c = 7sqrt(7)
I call this going backwards. Look at the number in front of the 7sqrt(2), it is 7. The sides a and b are both 7. Going backwards means divide.
--
EX: harder
a = ?, b = ? , c = 15
Remember, we are going backward from the hypotenuse to the legs, so we divide by sqrt (2) to get 15/sqrt(2). Don't know if you have sen these yet.
--
--
(ii) 30-60-90.
here it is a bit tricky, but here are the rules.
The side opposite 30 degrees is always 1/2 hypotenuse
The side opposite 60 degrees is always side opposite 30 number sqrt(3) glued on.
You can remember this as 30 -> sqrt(3) is needed.
--
EX:
a = 5, b = 5sqrt(3), c =
You can use Pythagorean theorem if desired here to get
10 = c.
Or remember to go forward means double side opposite 30 degree angle to get hypotenuse.
--
EX:
a = ? b = 8sqrt(3), c = 16
take 1/2 hypotenuse to get a = 8.
--
EX:
a = 10, b = ?, c = 20
take the 10 and glue a sqrt(3) to get 10sqrt(3)
whew! hope this helps, look through your book and do the odds - they are usually in the back.
|
|
|
