Trigonometry and Geometry Concepts

The video covers essential geometry topics needed for precalculus, including the distance and midpoint formulas, the Pythagorean theorem, special right triangles, trigonometric ratios, area calculations for polygons, and properties of quadrilaterals. It emphasizes the importance of understanding these concepts for building the unit circle and solving various geometric problems.

What is the distance between the points (1, -3) and (-5, 0)?

• √45

• 3√5

• 5√3

• 9

If the midpoint of a segment is (-2, -1.5), what are the coordinates of one endpoint if the other is (1, -3)?

• (-4, -1)

• (-1, -4)

• (-3, -2)

• (-5, 0)

Using the Pythagorean theorem, what is the length of the hypotenuse if the legs are 4 and 6?

• 2√13

• 13

• √52

• 4√13

In a 30-60-90 triangle, if the short leg is 10, what is the length of the hypotenuse?

• 15

• 5√3

• 10√3

• 20

For a 45-45-90 triangle, if one leg is 10, what is the length of the hypotenuse?

• 15

• 5√2

• 20

• 10√2

What is the sine of an angle in a right triangle if the opposite side is 4 and the hypotenuse is 10?

• 0.6

• 0.4

• 0.8

• 0.5

If the tangent of an angle is 3/4, what is the ratio of the opposite side to the adjacent side?

• 2:3

• 1:1

• 4:3

• 3:4

What is the area of a rectangle with a length of 5 and a width of 3?

• 10

• 15

• 12

• 8

Which property is true for all parallelograms?

• All angles are right angles

• Opposite sides are parallel

• Diagonals are perpendicular

• Diagonals are equal

What is the formula for the area of an equilateral triangle with side length s?

• s²/4

• s²√2/4

• s²/2

• s²√3/4