Challenge yourself with key concepts from ACT Math, focusing on essential geometry and trigonometry skills. This quiz covers triangles, circles, angles, and right triangle trigonometry to help you prepare effectively for the ACT.
In a triangle, the two known angles measure 48° and 62°. What is the measure of the third angle?
Explanation: The sum of the angles in any triangle is always 180 degrees. Subtracting the sum of 48 and 62 from 180 gives 70 degrees, so the answer is 70°. The option 90° suggests a right triangle, which is incorrect here, and 82° or 100° would both make the sum exceed 180°. Only 70° provides a sum of exactly 180°.
What is the area of a circle with a radius of 7 units?
Explanation: The formula for the area of a circle is π times the radius squared, so π*(7²) equals 49π. The answer 14π may confuse circumference with area, while 21π is a common computation mistake multiplying radius and π. Choosing 7π ignores the squared aspect that is essential when calculating area.
A right triangle has legs of lengths 6 and 8. What is the length of the hypotenuse?
Explanation: Applying the Pythagorean theorem: 6² + 8² = 36 + 64 = 100; the square root of 100 is 10, so the hypotenuse is 10. The answer 12 results from incorrectly adding the legs, 14 and 16 both exceed the actual value and might result from calculation errors. Only 10 meets the theorem conditions.
How many degrees are in the sum of the interior angles of a pentagon?
Explanation: For any n-sided polygon, the sum of the interior angles is 180 times (n-2). For a pentagon, that's 180*(5-2) = 540°. The answer 360° refers to the sum of the exterior angles, 720° is for a hexagon, and 900° is too high, possibly from multiplying by incorrect factors.
Which trigonometric ratio correctly gives the sine of a 30° angle in a right triangle?
Explanation: The sine function for a given angle is defined as the length of the side opposite the angle divided by the hypotenuse of the triangle. Adjacent over Hypotenuse is the definition for cosine, Opposite over Adjacent is tangent, and Hypotenuse over Opposite is the reciprocal of sine, or cosecant. Only Opposite over Hypotenuse is correct for sine.