One of the base angles of an isosceles triangle is 40 then the other two angles are

Isosceles triangle calculator is the best choice if you are looking for a quick solution to your geometry problems. Find out the isosceles triangle area, its perimeter, inradius, circumradius, heights and angles - all in one place. If you want to build a kennel, find out the area of Greek temple isosceles pediment or simply do your maths homework, this tool is here for you. Experiment with the calculator or keep reading to find out more about the isosceles triangle formulas.

An isosceles triangle is a triangle with two sides of equal length, which are called legs. The third side of the triangle is called base. Vertex angle is the angle between the legs and the angles with the base as one of their sides are called the base angles.

Properties of the isosceles triangle:

• it has an axis of symmetry along its vertex height
• two angles opposite to the legs are equal in length
• the isosceles triangle can be acute, right or obtuse, but it depends only on the vertex angle (base angles are always acute)

The equilateral triangle is a special case of a isosceles triangle.

To calculate the isosceles triangle area, you can use many different formulas. The most popular ones are the equations:

1. Given arm a and base b:

   area = (1/4) * b * √( 4 * a² - b² )

2. Given h height from apex and base b or h2 height from other two vertices and arm a:

   area = 0.5 * h * b = 0.5 * h2 * a

3. Given any angle and arm or base

area = (1/2) * a * b * sin(base_angle) = (1/2) * a² * sin(vertex_angle)

Also, you can check our triangle area calculator to find out other equations, which work for every type of the triangle, not only for the isosceles one.

To calculate the isosceles triangle perimeter, simply add all the triangle sides:
perimeter = a + a + b = 2 * a + b

Isosceles triangle theorem, also known as the base angles theorem, claims that if two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Also, the converse theorem exists, stating that if two angles of a triangle are congruent, then the sides opposite those angles are congruent.

A golden triangle, which is also called sublime triangle is an isosceles triangle in which the leg is in the golden ratio to the base:

a / b = φ ~ 1.618

The golden triangle has some unusual properties:

• It's the only triangle with three angles in 2:2:1 proportions
• It's the shape of the triangles found in the points of pentagrams
• It's used to form a logarithmic spiral

Let's find out how to use this tool on a simple example. Have a look at this step-by-step solution:

1. Determine what is your first given value. Assume we want to check the properties of the golden triangle. Type 1.681 inches into leg box.
2. Enter second known parameter. For example, take a base equal to 1 in.
3. All the other parameters are calculated in the blink of an eye! We checked for instance that isosceles triangle perimeter is 4.236 in and that the angles in the golden triangle are equal to 72° and 36° - the ratio is equal to 2:2:1, indeed.

You can use this calculator to determine different parameters than in the example, but remember that there are in general two distinct isosceles triangles with given area and other parameter, e.g. leg length. Our calculator will show one possible solution.

The smallest two angles in every triangle are acute angles (have measure less than 90�). Sometimes the largest angle is also acute (has measure less than 90�), sometimes it is right (has measure exactly 90�). and sometimes it is obtuse (has measure greater than 90�). If the largest angle is also an acute angle, the triangle is said to be "an acute triangle". If the largest angle is a right angle, the triangle is said to be "a right triangle". If the largest angle is an obtuse angle, the triangle is said to be "an obtuse triangle". The triangle yoiu are talking about is isosceles with a base angle of 40�. So we draw it:

Now since it is isosceles, we know that the other base angle is also 40�. So we label it 40� also They are both acute angles since 40� is less than 90�. So we need to know about the largest angle, which is the vertex angle of the isosceles triangle. We can look and see that it looks like it's obtuse, but in geometry, we can't go by "what it looks like is true". We have to prove it. Let's suppose the vertex angle is x�. Since we know the three interior angles of every triangle totals 180�, we have: x� + 40� + 40� = 180� We combine the terms 40� and 40� and get 80� x� + 80� = 180� We subtract 80� from both sides and get x� = 100� Since 100� is more than 90� the largest angle is obtuse, and so the triangle is an obtuse triangle. Edwin

Wine M.

asked • 01/07/20

Please provide an easy, short explanation for me to understand too if you can, thank you so much

1 Expert Answer

Mark H. answered • 01/07/20

Tutoring in Math and Science at all levels

The three angles of any triangle must total 180 degrees.

By definition, an isoceles triangle must have 2 equal sides, and therefore 2 equal angles.

Two possibilities:

1. A 40 degree angle at each side, and a 100-degree angle at the top.
2. A 40-degree angle at the top, and a 70-degree angle at each side

Draw each one--approximately to scale--so you can visualize