Use the table below for values of

\cos (\theta)

and

\sin (\theta)

\begin{array}{|c|l|l|}\hline \theta(\text { degrees }) & \cos (\boldsymbol{\theta}) & \sin (\boldsymbol{\theta}) \\\hline 10 & 0.985 & 0.174 \\\hline 20 & 0.940 & 0.342 \\\hline 30 & 0.866 & 0.500 \\\hline 40 & 0.766 & 0.643 \\\hline 45 & 0.707 & 0.707 \\\hline 50 & 0.643 & 0.766 \\\hline 60 & 0.500 & 0.866 \\\hline 70 & 0.342 & 0.940 \\\hline 80 & 0.174 & 0.985 \\\hline\end{array}

A projectile is launched with an initial velocity of

150 \mathrm{ft} / \mathrm{s}

from a height of 30 feet above the ground.
a) Complete the table by filling in the time required for the projectile to land. Round to the nearest hundredth of a second.

\begin{array}{|l|l|}\hline \boldsymbol{\theta} \text { (degrees) } & \text { Time }(s) \\\hline 10 & \\\hline 30 & \\\hline 50 & \\\hline 70 & \\\hline\end{array}

b) What launch angle gives the projectile the longest time in the air?
c) Complete the table by filling in the distance traveled horizontally by the projectile. Use the times found in part a. Round to the nearest hundredth of a foot.

\begin{array}{|l|l|}\hline \boldsymbol{\theta} \text { (degrees) } & \text { Distance }(\text { ft }) \\\hline\end{array}

d) What launch angle gives the greatest horizontal distance?
A)
a)

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 3.72 \\\hline 30 & 6.19 \\\hline 50 & 8.93 \\\hline 70 & 9.41 \\\hline\end{array}

70^\circ

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 411.87 \\\hline 30 & 698.63 \\\hline 50 & 571.08 \\\hline 70 & 493.77\\\hline \end{array}

30^\circ

B)
a)

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 10.86 \\\hline 30 & 8.64 \\\hline 50 & 7.43 \\\hline 70 & 5.83 \\\hline\end{array}

10^\circ

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 676.55 \\\hline 30 & 732.71 \\\hline 50 & 786.62 \\\hline 70 & 825.83 \\\hline\end{array}

70^\circ

C)
a)

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 1.68 \\\hline 30 & 3.81 \\\hline 50 & 3.96 \\\hline 70 & 1.95\\\hline\end{array}

50^\circ

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 683.07 \\\hline 30 & 521.65 \\\hline 50 & 519.96 \\\hline 70 & 417.38 \\\hline\end{array}

10^\circ

D)
a)

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 2.41 \\\hline 30 & 5.06 \\\hline 50 & 7.43 \\\hline 70 & 9.02 \\\hline\end{array}

70^\circ

\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 356.08 \\\hline 30 & 657.29 \\\hline 50 & 716.62 \\\hline 70 & 462.73 \\\hline\end{array}

50^circ

Solve by Using the Quadratic Formula - 2x2+10x=−42 x^{2}+10 x=-42x2+10x=−4 A) {−10±172}\left\{\frac{-10 \pm \sqrt{17}}{2}\right\}{2−10±17​​}

Multiple Choice

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Solve by Using the Quadratic Formula
- $2 x^{2}+10 x=-4$ A) $\left\{\frac{-10 \pm \sqrt{17}}{2}\right\}$

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