| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.52 |
| Score | 0% | 70% |
Order the following types of angle from least number of degrees to most number of degrees.
right, acute, obtuse |
|
right, obtuse, acute |
|
acute, right, obtuse |
|
acute, obtuse, right |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
If the area of this square is 25, what is the length of one of the diagonals?
| 9\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 52 + 52
c2 = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)
If angle a = 50° and angle b = 65° what is the length of angle c?
| 65° | |
| 87° | |
| 99° | |
| 76° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 50° - 65° = 65°
If side a = 5, side b = 8, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{10} \) | |
| \( \sqrt{61} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{20} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 82
c2 = 25 + 64
c2 = 89
c = \( \sqrt{89} \)
If AD = 15 and BD = 10, AB = ?
| 6 | |
| 10 | |
| 1 | |
| 5 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD