Question

A right triangle has a leg with a length of 21 units and a hypotenuse with a length of 42 units. Eunice states that because the hypotenuse is twice the length of the given leg, the right triangle is a 30-60-90 triangle. Select all statements that are true.
1. The measure of the remaining leg is 21$\sqrt{3}$ units
2. The angle opposite the side with length 21 units measures 30°
3. The perimeter of the triangle is 84 units
4. Eunice is not correct. It is a 45-45-90 triangle.
5. The measure of the remaining leg is 21 units.

Thank you! Whoever answers correctly gets 15 points!

Answer 1

Answer:

1. The measure of the remaining leg is 21\sqrt{3} units

2. The angle opposite the side with length 21 units measures 30°

Step-by-step explanation:

The Pythagorean theorem tells you the remaining side length is ...

  √(42² -21²) = 21√3 . . . . . matches the first statement, discounts statements 3 and 5

The angle opposite the 21-unit leg can be found from ...

  angle = arcsin(21/42) = 30° . . . . . matches the second statement, discounts statement 4.