Question

Is the triangle drawn by Darren a 30°–60°–90° triangle? How do you know?

A. Yes, because the sum of its angles is 180 degrees.
B. No, because it has unequal sides.
C. Yes, because it has a 60-degree angle.
D. No, because it lacks a right angle.

Answer 1

To determine if a triangle is a 30°–60°–90° triangle, we need to check if it satisfies the conditions of this special triangle.

Step-by-step explanation:

A 30°–60°–90° triangle is a special type of right triangle where one angle measures 30 degrees, another angle measures 60 degrees, and the remaining angle is a right angle of 90 degrees. To determine if the triangle drawn by Darren is a 30°–60°–90° triangle, we need to check if it satisfies the conditions of this special triangle.

If the triangle has a 60-degree angle and its sides follow a specific ratio, then it is a 30°–60°–90° triangle. The sides of a 30°–60°–90° triangle have a ratio of 1:√3:2. This means that the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3 times the length of the shorter side.

So, to determine if Darren's triangle is a 30°–60°–90° triangle, we need to measure the lengths of its sides and check if they follow the ratio 1:√3:2.