The leg of a right triangle that lies on one ray of angle θ is called the ___ leg, and the leg that lies across triangle from θ is called the ___ leg.

Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)

Find the point on the line $y=5x+3$ that is closet to the origin.

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter(A,B, C, D or E)in each blank
A . ${\displaystyle \tan \left(\arcsin \left(\frac{x}{8}\right)\right)}$
B . ${\displaystyle \cos \left(ar\sin \left(\frac{x}{8}\right)\right)}$
C. ${\displaystyle \left(\frac{1}{2}\right)\sin \left(2\arcsin \left(\frac{x}{8}\right)\right)}$
D. ${\displaystyle \sin \left(\arctan \left(\frac{x}{8}\right)\right)}$
E. ${\displaystyle \cos \left(\arctan \left(\frac{x}{8}\right)\right)}$

Jamie was supposed to have completed a portfolio of geometric constructions during spring break. She started this construction of a triangle center on the first day of her vacation and then forgot about it. Help her complete her portfolio entry. What is the name of the triangle center that Jamie constructed (point X )? What special properties does it have? Compute the volume of the figure at right.

Find the remaining angles for ${\displaystyle △ABC}$. ${\displaystyle m\angle B=30\circ \text{and}m\angle A=\frac{1}{2}m\angle C}$
${\displaystyle m\angle A=\surd \circ }$ and ${\displaystyle m\angle C=\surd \circ }$

At what point do the curves ${\displaystyle r_1\left(t\right)=t,4-t,35+t^2}$ and ${\displaystyle r_2\left(s\right)=7-s,s-3,s^2}$ intersect? (x,y,z)= Find angle of intersection, ${\displaystyle \theta }$, correct to the nearest degree.

At what point do the curves $r_1(t)=t,4-t,35+t^2$ and $r_2(s)=7-s,s-3,s^2$ intersect? (x,y,z)= Find angle of intersection, $\theta$, correct to the nearest degree.