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Can a Triangle have 1 right angle and 3 equal sides?

Answer 1

Only if it is a curvilinear triangle.

If an ordinary planar triangle is equilateral (having equal sides), then it will also be equiangular (having equal angles) and those angles will sum to #pi# radians (#180^@#), so each internal angle will be #pi/3# radians (#60^@#).

On the other hand a curvilinear triangle on the surface of a sphere could have #3# right angles and #3# equal sides if the length of each side is #1/4# of the circumference of the sphere.

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Answer 2

Savannah Aguilar

No, a triangle cannot have one right angle and three equal sides simultaneously. In a triangle, if one angle is a right angle (90 degrees), the other two angles must be acute angles (less than 90 degrees) because the sum of the interior angles of a triangle is always 180 degrees. Additionally, if a triangle has three equal sides, it must also have three congruent angles, which would necessitate each angle to measure 60 degrees (since the sum of the angles in an equilateral triangle is 180 degrees divided by 3). Therefore, it is not possible for a triangle to have one right angle and three equal sides.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.