SOLUTION: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Click here to see ALL problems on Triangles

Question 480043: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Found 4 solutions by Theo, ikleyn, Edwin McCravy, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
the base angles of an isosceles triangle are equal so the sum of the 2 base angles is equal to 120 degrees.
the sum of all 3 angles of a triangle is 180 degrees, so the third angle is 180 - 120 = 60 degrees.
in this case your isosceles triangle becomes an equilateral triangle.
all 3 sides are equal.
all 3 angles are equal.
because 2 sides and 2 angles are equal, it is an isosceles triangle.
because 3 sides and 3 angles are equal, it is an equilateral triangle.
the answer to your question, however, is simply that the vertex angle is 60 degrees if one of the base angles is 60 degrees for the reasons outlined above.

Answer by ikleyn(52898)   (Show Source):
You can put this solution on YOUR website!
.
what is the measure of the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The formulation of this problem is below floor level, i.e. is completely absurdist.

In Euclidean geometry on the plane, there is such an isosceles right triangle
with one of its base angle measure of 60 degrees.

*******************************************************************

                    Simply the composer, who creates such problems,
         is TOTALLY and FATALLY illiterate and incompetent in Math.

*******************************************************************

As tutor @Theo solves this problem, leaving without his comments or corrections
the fact that the problem's formulation is incorrect, it forces me to assume
that @Theo either did not read the problem or did not understand what was written in the post.

In this form, the problem is so , that its only place is in a garbage bin.

It is also good for scaring people on Halloween.

Serious to the creator of this problem for his or her complete incompetence in Math.

                The interesting fact is that an isosceles right triangle with base angles of 60 degrees
                can exist on a sphere. This is possible in spherical geometry,
                which differs significantly from Euclidean (flat plane) geometry.

                I'm saying this to cheer you up and make you laugh.

Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!

Every isosceles right triangle, a.k.a, a 45-45-90 right triangle, is half a square cut down a diagonal. Draw a square, which has 4 interior 90^o angles. Cut it down one of the diagonals: Take the left half of the square: The triangle above is an isosceles right triangle. Notice that its vertex angle is 90^o and each base angle is 45^o. As you see, the base angles CANNOT be as you have stated. Edwin

Answer by greenestamps(13214)   (Show Source):
You can put this solution on YOUR website!

There is no isosceles right triangle with a base angle that measures 60 degrees. In an isosceles right triangle, the vertex angle is 90 degrees and each base angle is 45 degrees.

In an isosceles triangle with one base angle 60 degrees, the other base angle is 60 degrees, so the sum of the two base angles is 120 degrees. Then, since the sum of the angles of a triangle is 180 degrees, the measure of the vertex angle is 180-120 = 60 degrees. So if the statement of the problem was supposed to state "isosceles triangle" instead of "isosceles right triangle", the answer is that the vertex angle is 60 degrees.

But as the problem is posted, with an "isosceles right triangle", the problem is faulty and has no solution.