You will also need the angles so that you can use the Isosceles Triangle Theorems to solve for the base of isosceles triangle when only two sides are given.
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.
It depends on the infoamtion that you have.
Correct as would be the case for an isosceles triangle or an equilateral triangle
First find 180 minus the vertex angle and divide that by 2 to get the other angles. Then solve the other sides by using sin(vertex angle)/base=sin(other angles)/other sides.
It means to find all of its sides and angles.
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.
It depends on the infoamtion that you have.
It depends on the details of the specific triangle.
Correct as would be the case for an isosceles triangle or an equilateral triangle
If you know the length of the sides, you can use Pythagoras' Theorem to calculate the height. Use half the base for one of the shorter sides, and either of the two identical sides of the triangle for the hypothenuse. Solve for the other one of the shorter sides (the height).
First find 180 minus the vertex angle and divide that by 2 to get the other angles. Then solve the other sides by using sin(vertex angle)/base=sin(other angles)/other sides.
You cannot - unless there is some other information. For example, that the triangle is isosceles, or that one of the shorter sides is related to the other is some way. Or there is another triangle (or other shape) from which you can work out one of the sides.
Two sides, or two angles + one side.
Given the lengths of two sides of a right triangle, you can find the length of the other side.
Square the two smaller sides and add them together. Take the square root of the answer. If that is the same as the third side then you have a right angled triangle and if not, then you have not.
Use the sine rule to work out one of the sides. (a/sina = b/sinb = c/sinc) Then as it is an isosceles triangle the perpendicular dropped from the apex will (a) bisect the base and (b) form a right angle with the base. Now you know one side and the hypotenuse of a right-angled triangle and you use Pythagoras (a2 + b2 = c2) to solve the 'other' side of that, which is the height of the isosceles triangle.
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