△ABC has a>b>c. If one of the angles in the triangle is 60°, name the angle that can be equal to 90°.

Accepted Solution

Answer:The angle that can be equal to 90° will be [tex]\angle A[/tex] or [tex]\angle BAC[/tex]Step-by-step explanation:[tex]\triangle ABC[/tex]  has  [tex]a>b>c[/tex]. That means, the longest side is  [tex]a[/tex] and the shortest side is [tex]c[/tex]As the sum of all angles in a triangle is 180°, then if two angles are 60° and 90°, so the third angle will be:  [tex]180\°-(60\°+90\°)= 180\°-150\°= 30\°[/tex]Now, we know that the measure of opposite angle to the longest side is the largest angle. As here side [tex]a[/tex] is the longest side, so [tex]\angle A[/tex] or [tex]\angle BAC[/tex] will be the largest angle which is 90°