SAT Math Unit 4: Geometry and Trigonometry

A circle has a radius of $7$. What is the circumference of the circle? (Use $\pi \approx 3.14$.)

In a right triangle, one acute angle measures $30°$. The hypotenuse has length $10$. What is the length of the side opposite the $30°$ angle?

In the unit circle, angle $\theta$ is in standard position and $\cos \theta =-\frac{\sqrt{2}}{2}$ with $\sin \theta >0$. In which quadrant does angle $\theta$ lie?

In the figure, line $\ell$ is parallel to line $m$. A transversal crosses both lines, creating alternate interior angles. One alternate interior angle measures $(3x+10)°$ and the other measures $(5x-20)°$. What is the value of $x$?

In right triangle $ABC$, angle $C$ is the right angle, $AC=8$, and $BC=6$. What is $\cos (A)$?

A sphere has a radius of $6$. What is its volume? (Leave in terms of $\pi$.)

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

A cylinder has radius $r=3$ and height $h=5$. What is its volume? (Leave in terms of $\pi$.)

A rectangle has length $l$ and width $w$. If the length is doubled and the width is halved, how does the area change?

Two lines intersect and form a pair of vertical angles. One angle measures $47°$. What is the measure of its vertical angle?

What is the area of a triangle with base $10$ and height $6$?

A point $P$ is at coordinates $(3,-4)$. What is the distance from $P$ to the origin?