Examples of Right Triangle Trigonometry

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

Solving Multl-Step Equations (continued)

Veronica made a triangle by taking an 8 $\frac{1}{2}\times 11$ sheet of paper and putting a dot at the top. She then drew lines from the bottom corners to the dot and cut along the lines (see diagram).
What is the area of the triangle that Veronica cut out?

If the hypotenuse of a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle has a length of ${\displaystyle \sqrt{2}}$, how long are the legs?

In triangle ABC, $a=15$, $b=14$, $c=10$. Find ${\displaystyle m<B}$

Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is ${60}^{\circ }$, how far are you from the base of the plateau?

In general, $\tan (\alpha +\beta )$ is not equal to $\tan \alpha +\tan \beta$. However, there are some values of $\alpha$ and $\beta$ for which they are equal. Find such $\alpha$ and $\beta$ and do the same for $\tan (\alpha -\beta )$

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

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.