I have a triangle with a 90 degree angle and then two 45 degree angles. I know the hypotenuse is 14, how do I solve for both sides, IN SIMPLIFIED RADICAL FORM. Thank you for the help!
Also, I have another triangle with a right angle and a 60 degree measured angle as well. The side that is opposite the 60 degree angle is 21, how do I figure out the other two sides, in simplified radical from?
Lastly, I have another triangle, a right triangle with a 30 degree angle. The side adjacent to that is 33. How do I find the other two sides in simplified radical form?
Thanks so much!
Also, I have another triangle with a right angle and a 60 degree measured angle as well. The side that is opposite the 60 degree angle is 21, how do I figure out the other two sides, in simplified radical from?
Lastly, I have another triangle, a right triangle with a 30 degree angle. The side adjacent to that is 33. How do I find the other two sides in simplified radical form?
Thanks so much!
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45-45-90 triangles are in ratio of 1-1-sqrt2 (sides opposite corresponding angles)
30-60-90 triangles are in ratio of 1-sqrt3-2
You should just remember these. It will make your life much easier.
Ok, now to your problems.
In a 45-45-90 triangle, if the hypoteneuse is 14, then the legs must both be 14 / sqrt(2)
Some teachers want you to remove any radicals from the denominator, though.
If so simply multiply in this case by sqrt(2) / sqrt(2)
You will come up with 14 * sqrt(2) / 2 or 7*sqrt(2)
For the next, the 21 is the longest leg, so the short side must be 21 / sqrt(3) or 7*sqrt(3)
The last one is essentially the same problem as the second.
The short leg must be 33 / sqrt(3) or 11*sqrt(3)
Seriously, though. Just memorize those ratios and your life will be much easier for it.
30-60-90 triangles are in ratio of 1-sqrt3-2
You should just remember these. It will make your life much easier.
Ok, now to your problems.
In a 45-45-90 triangle, if the hypoteneuse is 14, then the legs must both be 14 / sqrt(2)
Some teachers want you to remove any radicals from the denominator, though.
If so simply multiply in this case by sqrt(2) / sqrt(2)
You will come up with 14 * sqrt(2) / 2 or 7*sqrt(2)
For the next, the 21 is the longest leg, so the short side must be 21 / sqrt(3) or 7*sqrt(3)
The last one is essentially the same problem as the second.
The short leg must be 33 / sqrt(3) or 11*sqrt(3)
Seriously, though. Just memorize those ratios and your life will be much easier for it.
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I have a triangle with a 90 degree angle and then two 45 degree angles. I know the hypotenuse is 14, how do I solve for both sides, IN SIMPLIFIED RADICAL FORM. Thank you for the help!
**with a 45-45 triangle, the hypotenuse is always rad 2 times bigger than the congruent legs, so the legs have to be 7 rad 2. You can divide the hypotenuse by rad 2 to get the answer, but be sure to rationalize the fraction.
Also, I have another triangle with a right angle and a 60 degree measured angle as well. The side that is opposite the 60 degree angle is 21, how do I figure out the other two sides, in simplified radical from?
**with a 30-60 triangle, the hypotenuse is always twice as big as the smallest side (which is opposite the 30 degree angle. and the middle side is always rad 3 times the smallest side. So you have to divide the middle side by rad 3 to get the smallest side, which is 7 rad 3...and double that to get the hypotenuse, which is 14 rad 3.
It is much easier to see the pattern in solving these with live examples rather than someone trying to type out the process. I hope this did not confuse you even further.
good luck with the rest
**with a 45-45 triangle, the hypotenuse is always rad 2 times bigger than the congruent legs, so the legs have to be 7 rad 2. You can divide the hypotenuse by rad 2 to get the answer, but be sure to rationalize the fraction.
Also, I have another triangle with a right angle and a 60 degree measured angle as well. The side that is opposite the 60 degree angle is 21, how do I figure out the other two sides, in simplified radical from?
**with a 30-60 triangle, the hypotenuse is always twice as big as the smallest side (which is opposite the 30 degree angle. and the middle side is always rad 3 times the smallest side. So you have to divide the middle side by rad 3 to get the smallest side, which is 7 rad 3...and double that to get the hypotenuse, which is 14 rad 3.
It is much easier to see the pattern in solving these with live examples rather than someone trying to type out the process. I hope this did not confuse you even further.
good luck with the rest