A triangle has a side length of 5.2

Question

feet, an angle of 71.8∘,
and another angle of 54.1∘.

Which statements about this triangle are true?

Select three that apply.

Responses

This is a right triangle.
This is a right triangle.

This cannot be an equilateral triangle.
This cannot be an equilateral triangle.

This is an isosceles triangle.
This is an isosceles triangle.

This is an obtuse triangle.
This is an obtuse triangle.

This is a scalene triangle.
This is a scalene triangle.

This triangle has a third angle with a measure of 54.1∘.

Answer 1

Given the angles provided, we can find certain characteristics of the triangle. The angles of the triangle are:

• Angle A = 71.8°
• Angle B = 54.1°
• To find Angle C, we use the triangle sum theorem (the sum of the angles in a triangle is 180°):

\[ \text{Angle C} = 180° - (71.8° + 54.1°) = 180° - 125.9° = 54.1° \]

With this information, we can evaluate the statements:

1. This is a right triangle.
   False. A right triangle has one angle measuring 90°, and none of the angles here do.

2. This cannot be an equilateral triangle.
   True. An equilateral triangle has all three angles equal, and here the angles are 71.8° and two angles of 54.1°.

3. This is an isosceles triangle.
   True. The triangle has two angles that are equal (the two angles of 54.1°), which makes it isosceles.

4. This is an obtuse triangle.
   False. An obtuse triangle has one angle greater than 90°, and the angles provided do not exceed 90°.

5. This is a scalene triangle.
   False. A scalene triangle has all sides of different lengths, but this triangle has at least two angles that are the same (the two 54.1° angles).

6. This triangle has a third angle with a measure of 54.1°.
   True. From our calculations, the third angle measures 54.1°.

Based on the analysis, the true statements are:

• This cannot be an equilateral triangle.
• This is an isosceles triangle.
• This triangle has a third angle with a measure of 54.1°.