# Triangle DEF has side lengths of 8 cm, 10 cm, and 9 cm. Use the relationship between the sides and angles of a triangle to match each side with its correct length. 3giez4
Hello there!

1) Solving a right triangle means finding the values of the unknown {most likely a variable}
2) The picture is for the Similarity in Right Triangles, I couldn't explain it.
How you can use Pythagorean Theorem: The formula for that is (a^2 + b^2 = c^2). The longest side of a triangle is called the hypotenuse, and the other sides are called legs. You usually use Pythagorean Theorem when you are trying to find an angle of a side. A and B in the formula are the legs and C is the hypotenuse, it makes sense because the hypotenuse is the longest side of the triangle, which means that it has a greater angle than the legs. So say you have a triangle with a leg of 5, a leg of 7, and the hypotenuse is unknown. (If you're a visual person, I also drew it on paint and put it in :P) The formula is a^2 + b^2 = c^2. The ^2 is an exponent, which means that we have to multiply the base by itself that many times. For example, if we had 3^4, we'd have to multiply 3   4 times. (3*3*3*3=81) So 5*5=25 and 7*7=49. It would be better it fill in the formula as you go. So now you have (25+49=c^2). You wouldn't multiply c^2, because we don't know the base yet, it's an unknown, so we keep it at that for a while. So now we just continue with the problem which is basically 25+49 which is 74. (74=c^2) But that's not the answer. We have to find the square root of 74 in order to get the answer because we have to multiply with an exponent, the opposite is square rooting which is what we have to do. (((what sucks is that I reached the max of files to enter for you so your just gonna have to read the rest. sorry))) So the square root of 74 is 8.6. And that's your answer. The legs are 5 and 7, and your hypotenuse is 8.6. But what if you need to find one of the legs. The formula would be a= ( I hope the insert thing works if it doesn't I said a= square root of c^2-b^2)
I hope you can solve that because I have to go to a testing Class Connect, and I don't think I've learned the other questions yet. I'm sorry, and I hope I've helped!!      bree249

The answer is side and angle measures must be congruent! Hope this helped :)

Step-by-step explanation: Haven263
1. WHAT DOES IT MEAN TO SOLVE A RIGHT TRIANGLE?  Every triangle has 3 angles and 3 sides.  A right triangle has one 90-degree angle and a hypotenuse, the side opposite the right triangle.

To "solve a right triangle," we must come up with the length of each of the 3 sides and the measures of the 2 angles beyond the 1 right triangle.

Example:  Given the right triangle with one of the smaller angles equal to 30 degrees and hypotenuse equal to 7, "solve" the triangle.  In other words, find the lengths of the 2 legs and the measure of the 3rd angle.  That angle is 90-30, or 60 degrees.  Thus, you have a 30-60-90 triangle.

One way to "solve" this triangle is to use the Law of Sines:

a            b              c
= =
sin A      sin B       sin C.

If we let c = 7 and C = 90 deg, then the side length opposite the 30 degree angle is

a             7
=
sin 30     sin 90

and this simplifies to a(1) = (7)(sin 30) = 7/2

So now we know that one angle is 90 degrees, one is 30 and one is 60.

The 7 inch hypotenuse is opposite the 90 degree angle; the side opposite the 30 degree angle is 7/2, and the side opp. the 60 degree angle is 7sqrt(3)/2.  ### Other questions on the subject: Mathematics Mathematics, 21.06.2019, RoyalGurl01
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