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Using trigonometry and Pythagoras' theorem.

Q: How do you find the side measurements of a right triangle given one angle and one side?

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It is a scalene triangle other than a right angle triangle

In a right triangle, all the angle measurements together add up to be 180 degrees. And since it is a right triangle, one of the three angles is 90 degrees so if you are given one of the angles other than the right angle's measurements, you can find the angle measurements. Here's an example: There is a right triangle. One angle measures to be 45 degrees. What is the missing angle measure? Well we know that one angle must be 90 degrees and the other (as we were told) is 45 degrees. 90+45=135 and we know that a right triangle=180 degrees total and 180-135= 45. The missing angle is equal to 45 degrees! hope this makes sense and it helped.

Simply because the Pythagorean Theorem is not true for any triangle that doesn't have a right angle in it. If a triangle has a right angle in it, then it satisfies the Theorem. If it hasn't, then it doesn't. And if it satisfies the Theorem, then it has a right angle in it, and if it doesn't, then it hasn't.

It will be a right angled triangle with angles of 90, 72 and 18 degrees.

Yes the given dimensions complies with Pythagoras' theorem for a right angle triangle.

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It is a scalene triangle other than a right angle triangle

In a right triangle, all the angle measurements together add up to be 180 degrees. And since it is a right triangle, one of the three angles is 90 degrees so if you are given one of the angles other than the right angle's measurements, you can find the angle measurements. Here's an example: There is a right triangle. One angle measures to be 45 degrees. What is the missing angle measure? Well we know that one angle must be 90 degrees and the other (as we were told) is 45 degrees. 90+45=135 and we know that a right triangle=180 degrees total and 180-135= 45. The missing angle is equal to 45 degrees! hope this makes sense and it helped.

To circumscribed a circle about a triangle you use the angle. This is to get the right measurements.

A right angle triangle or an isosceles triangle.

Simply because the Pythagorean Theorem is not true for any triangle that doesn't have a right angle in it. If a triangle has a right angle in it, then it satisfies the Theorem. If it hasn't, then it doesn't. And if it satisfies the Theorem, then it has a right angle in it, and if it doesn't, then it hasn't.

I'm not sure what you are asking, so I may not be answering your question, but I'll try to the best of my ability.This is only for RIGHT TRIANGLESGiven a right triangle and the angle measurements besides the 90 degree angle of the right angle are 30 and 60 degrees (the combined angle measurements of a triangle always equal 180 degrees), the base is x, the height is xsqrt3, and the hypotenuse (or the longest side opposite the height) is 2x. This shortcut only works for right triangles with the other angle measurements 30 and 60 degrees.For example, you are given a triangle with the base=2 units. Using the shortcut, the height=2sqrt3 units. Then the hypotenuse=4 units.Given a right triangle and the angle measurements besides the 90 degree angle of the right angle are 45 and 45 degrees, the base is x, the height is also x, and the hypotenuse is xsqrt2. This shortcut only works for right triangles with both the other angle measurements equal to 45 degrees.For example, you are given a triangle with the base=2 units. The height is also 2 units. And finally, the hypotenuse=2sqrt2 units.*Another way to find the other side beside the shortcut is by using the Pythagorean Theorum (a2+b2=c2) if you are given the other two side measurements.*

The Hypotenuse.

It will be a right angled triangle with angles of 90, 72 and 18 degrees.

Yes the given dimensions complies with Pythagoras' theorem for a right angle triangle.

No because the given dimensions do not comply with Pythagoras; theorem for a right angle triangle.

A right angle triangle would fit the given description

The dimensions given fit that of a right angle triangle