Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and = base angle

So the equation to solve becomes .

The triangle has two sides of equal length, 13, so it is by definition isosceles.

To determine whether the triangle is acute, right, or obtuse, compare the sum of the squares of the lengths of the two shortest sides to the square of the length of the longest side. The former quantity is equal to

The latter quantity is equal to

The former is greater than the latter; consequently, the triangle is acute. The correct response is that the triangle is acute and isosceles.

The figure shows a right triangle. The acute angles of a right triangle have measures whose sum is , so

Substituting for :

This makes a 45-45-90 triangle. By the 45-45-90 Triangle Theorem, the length of leg is equal to that of hypotenuse , the length of which is 12, divided by . Therefore,

Rationalize the denominator by multiplying both halves of the fraction by :

By the same reasoning, .

The perimeter of the triangle is

The figure shows a right triangle. The acute angles of a right triangle have measures whose sum is , so

Substituting for :

This makes a 45-45-90 triangle. By the 45-45-90 Triangle Theorem, the length of leg is equal to that of hypotenuse , the length of which is 12, divided by . Therefore,

Rationalize the denominator by multiplying both halves of the fraction by :

By the same reasoning, .

The perimeter of the triangle is

To solve, simply use the formula for the diameter of a circle

where r is 5. Thus,

Remember, the diameter is the longest distance across a circle, and since the radius is 5, you can simply double that. Thus, the answer is 10.

The Pythagorean theorem is a2 + b2 = c2, where a and b are legs of the right triangle, and c is the hypotenuse.

(15)2 + (20)2 = c2 so c2 = 625. Take the square root to get c = 25m

Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and = base angle

So the equation to solve becomes .

The Pythagorean theorem is a2 + b2 = c2, where a and b are legs of the right triangle, and c is the hypotenuse.

(15)2 + (20)2 = c2 so c2 = 625. Take the square root to get c = 25m