Question

select the correct angle measures and side lengths for course 1, course 2, and course 3. course 1: 60°, 60°, 60°, 5 cm, 5 cm, 6 cm; course 1: 60°, 60°, 60°, 6 cm, 6 cm, 6 cm; course 1: 60°, 60°, 60°, 5 cm, 5 cm, 5 cm; course 1: 90°, 45°, 45°, 5 cm, 5 cm, 7 cm; course 2: 90°, 45°, 45°, 6 cm, 7 cm, 8.5 cm; course 2: 90°, 45°, 45°, 5 cm, 5 cm, 7 cm; course 2: 90°, 45°, 45°, 6 cm, 6 cm, 8.5 cm; course 2: 60°, 60°, 60°, 6 cm, 6 cm, 6 cm; course 3: 30°, 60°, 90°, 3 cm, 5 cm, 5 cm; course 3: 30°, 60°, 90°, 3 cm, 4 cm, 6 cm; course 3: 30°, 60°, 90°, 3 cm, 4 cm, 5 cm; course 3: 30°, 60°, 90°, 3 cm, 4 cm, 6 cm

Explanation:

Step1: Recall triangle properties

Equilateral triangles have all angles equal to 60° and all sides equal. Isosceles - right - triangles have angles 90°, 45°, 45°. Right - triangles with angles 30°, 60°, 90° have side - length ratios of 1:$\sqrt{3}$:2 (or multiples of these).

Step2: Analyze Course 1

For an equilateral triangle with all angles 60°, all sides should be equal. So Course 1 with angles 60°, 60°, 60° and side - lengths 6 cm, 6 cm, 6 cm is correct.

Step3: Analyze Course 2

For a right - isosceles triangle with angles 90°, 45°, 45°, if the legs (the sides adjacent to the 90° angle) are of length $a$, the hypotenuse $c$ is $a\sqrt{2}$. If the legs are 5 cm, the hypotenuse is $5\sqrt{2}\approx7$ cm. So Course 2 with angles 90°, 45°, 45°, side - lengths 5 cm, 5 cm, 7 cm is correct.

Step4: Analyze Course 3

For a 30° - 60° - 90° triangle, if the shortest side (opposite the 30° angle) is $a$, the hypotenuse is $2a$ and the other side is $a\sqrt{3}$. If the shortest side is 3 cm, the hypotenuse is 6 cm and the other side is $3\sqrt{3}\approx5$ cm is wrong. If the shortest side is 3 cm and the hypotenuse is 6 cm and the other side is $3\sqrt{3}\approx 5.2$ cm, a more accurate set with side - lengths 3 cm, 4 cm, 6 cm is wrong. The correct set for a 30° - 60° - 90° triangle with side - lengths in the ratio 1:$\sqrt{3}$:2 (multiplied by 2) is 3 cm, $3\sqrt{3}$ cm, 6 cm. But among the given options, the set with angles 30°, 60°, 90° and side - lengths 3 cm, 4 cm, 6 cm is the closest approximation considering the nature of the problem.

Answer:

Course 1: 60°, 60°, 60°, 6 cm, 6 cm, 6 cm
Course 2: 90°, 45°, 45°, 5 cm, 5 cm, 7 cm
Course 3: 30°, 60°, 90°, 3 cm, 4 cm, 6 cm