Find the length of a leg of an isosceles right triangle whose hypotenuse has length 12

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

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. ${\displaystyle \cos \left(\arctan \left(\frac{x}{8}\right)\right)}$

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

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-4,3), (0,5), and (3,-4)

The leg of a right triangle that lies on one ray of angle $\theta$ is called the ? leg, and the leg that lies across triangle from $\theta$ is called the ? leg.

If ${\displaystyle m\angle 1+m\angle 5=100}$, find the measure of ${\displaystyle \angle 2}$. ${\displaystyle A\left(\frac{1}{3}\right)2\left(\frac{4}{7}\right)=\left(\frac{8}{7}\right)8}$
${\displaystyle m\angle 2=\square =\frac{1}{9}}$ Type the correct answer, then press Enter.

${\displaystyle \cos \theta =\frac{9}{13}}$
${\displaystyle \sin \theta <0}$
1. ${\displaystyle \sin \theta =?}$
2. ${\displaystyle \tan \theta =?}$
3. ${\displaystyle \csc \theta =?}$
4. ${\displaystyle \sec \theta =?}$
5. ${\displaystyle \cot \theta =?}$