triangles topic

Question

In an isosceles triangle ABC ,AB=AC and angleABC=45(degrees) then length of BC is:

Answer 1

First, draw the triangle based on the info given.  An isosceles triangle has two congruent angles and two congruent sides.  Since the sum of the angles in a triangle is 180 degrees, and two angles are 45 degrees, then the other angle must be 90 degrees.  Thus, we have a right triangle.  Since each angle is 45, the equal sides AB and AC is 1 using the tangent function.  We use the tangent function because the hypotenuse is unknown. The hypotenuse is BC.  To find the length of BC, we can use the Pythagorean theorem.

 

BC = √(1² + 1²)

 

BC = √2