Study guides

☆☆

Q: How do you solve for the unknown side length for a right triangle?

Write your answer...

Submit

Still have questions?

Continue Learning about Geometry

An equilateral triangle hasn't a hypotenuse; hypotenuse means the side opposite the right angle in a right triangle. An equilateral triangle has no right angles; rather all three of its angles measure 60 degrees. Knowing the length of the hypotenuse of a right triangle does not give enough information to determine the triangle's height. But the length of a side (which is the same for every side) of an equilateral triangle is enough information from which to calculate the height of that triangle. The first way is simply to use the formula that has been developed for this purpose: height = (length X sqrt(3)) / 2. But you can also use the geometry of right triangles to solve for the height. That is because you can bisect the triangle with a vertical line from the top vertex to the center of the base. The length of that line, which splits the equilateral triangle into two right triangles, is the height of the equilateral triangle. We know a lot about each right triangle formed by bisecting the equilateral triangle: * - The hypotenuse length is the length of the equilateral triangle's side. * - The base length is half the length of the hypotenuse. * - The angle opposite the hypotenuse is 90 degrees. * - The angle opposite the vertical is 60 degrees (the measure of every angle of any equilateral triangle). * - The angle opposite the base is 30 degrees (half of the bisected 60-degree angle). * - (Note that the sum of the angles does equal 180 degrees, as it must.) Now to solve for the height of a right triangle. There are a few ways. For labeling, let's let h=height of the equilateral triangle and the vertical side of the right triangle; A=every angle of the equilateral triangle (each 60o); s=side length of any side of the equilateral triangle and thus the hypotenuse of the right triangle. Since the sine of an angle of a right triangle is equal to the ratio of the opposite side divided by the hypotenuse, we can write that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig tables you can now easily find the height.

This can only be done in the case of a right angle triangle. If 'x' represents one of the sides then the length of the two other sides must be known.

If it's a right angle triangle then use Pythagoras' theorem to find the 3rd side

It depends on what shape you have.

Area of the square if 36 cm2ExplanationSince a square has 4 sides of equal length, we solve this problem by finding the perimeter of the triangle and dividing that number by 4.We are given the lengths of the 3 sides so the perimeter is their sum. Sine the perimeter of the triangle is 24, we know the each side of the square is length 6.The area is 62 or 36

Related questions

There is not enough information to solve this. You need to know one other length od a side to solve this.

to find the unknown length of the longest side in a right angled triangle provided the length of the other two sides is known.

Assuming that you are talking about a right triangle. a2 + b2 = c2 Solve for a a = square root of c2-b2

Given the lengths of two sides of a right triangle, you can find the length of the other side.

the unknown measurement of a side of a triangle

Pythagorean theorum.

Make it a right triangle where one side of the right triangle is half the length of the non-identical side of the isosceles, the hypotenuse of the right triangle is the length of one of the identical sides of the isosceles triangle, then use the Pythagorean theorem. a^2+b^2=c^2. Where "a" is the length of one of the identical sides, and "c" is the length of half the non-identical sides. Solve for "b" and that is your height.

No. You need either another angle or the length of another side. For example, to solve a2 +b2=c2 (the formula for a right triangle, in which c is the hypotenuse) you must have values for 2 variables to solve for the third.

You use the Pythagorean theorem, which can only be applied to right triangles: a2+b2=c2, where a and b are the triangle's legs and c is the triangle's hypotenuse. Plug the two sides you know into the equation, then solve for the unknown side.

I'm having to go back a long time, but I don't remember being able to solve a triangle from one side and one angle...

An equilateral triangle hasn't a hypotenuse; hypotenuse means the side opposite the right angle in a right triangle. An equilateral triangle has no right angles; rather all three of its angles measure 60 degrees. Knowing the length of the hypotenuse of a right triangle does not give enough information to determine the triangle's height. But the length of a side (which is the same for every side) of an equilateral triangle is enough information from which to calculate the height of that triangle. The first way is simply to use the formula that has been developed for this purpose: height = (length X sqrt(3)) / 2. But you can also use the geometry of right triangles to solve for the height. That is because you can bisect the triangle with a vertical line from the top vertex to the center of the base. The length of that line, which splits the equilateral triangle into two right triangles, is the height of the equilateral triangle. We know a lot about each right triangle formed by bisecting the equilateral triangle: * - The hypotenuse length is the length of the equilateral triangle's side. * - The base length is half the length of the hypotenuse. * - The angle opposite the hypotenuse is 90 degrees. * - The angle opposite the vertical is 60 degrees (the measure of every angle of any equilateral triangle). * - The angle opposite the base is 30 degrees (half of the bisected 60-degree angle). * - (Note that the sum of the angles does equal 180 degrees, as it must.) Now to solve for the height of a right triangle. There are a few ways. For labeling, let's let h=height of the equilateral triangle and the vertical side of the right triangle; A=every angle of the equilateral triangle (each 60o); s=side length of any side of the equilateral triangle and thus the hypotenuse of the right triangle. Since the sine of an angle of a right triangle is equal to the ratio of the opposite side divided by the hypotenuse, we can write that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig tables you can now easily find the height.

true

People also asked