Question

math 2 unit 3 classwork name: thiago gonzalez soh cah toa directions - a.) find the value of x or θ in each problem below. round to the nearest tenth. b.) find the answer in the coloring sheet and color that piece according to \color\ that is associated to each set of problems. c.) you must show work to receive full credit for this worksheet! problem set #1 - color answers in this set blue problem set #2 - color answers in this set yellow problem set #3 - color answers in this set brown problem set #4 - color answers in this set red problem set #5 - color answers in this set orange problem set #6 - color answers in this set green

Explanation:

Step1: Recall SOH - CAH - TOA

$\text{SOH}:\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\text{CAH}:\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\text{TOA}:\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Use these ratios to find unknown sides or angles in right - triangles.

Step2: For Problem Set #1 (first triangle)

If we assume we know an angle $\theta$ and two sides of a right - triangle and we want to find an unknown side. For example, if we know an angle $\theta$ and the adjacent side and we want to find the opposite side, we use $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let's say in the first triangle of Problem Set #1, if we know $\theta$ and the adjacent side, and we want to find $x$ (opposite side), then $x = \text{adjacent}\times\tan\theta$.

Step3: General approach for all triangles

For each right - triangle, identify the known and unknown sides and angles. Then choose the appropriate SOH - CAH - TOA ratio. If we know two sides and want to find an angle, we use the inverse trigonometric functions. For example, if $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, then $\theta=\sin^{- 1}(\frac{\text{opposite}}{\text{hypotenuse}})$.

Answer:

Since the specific values of angles and sides for each triangle are not fully provided in a clear way in the text part (only some hand - written values are shown in the image which are not fully legible), we cannot give specific numerical answers for all the triangles. But the general method to find $x$ or $\theta$ in each right - triangle is to use the SOH - CAH - TOA ratios as described above. For example, if in a right - triangle with an angle $\theta$, adjacent side $a$ and opposite side $x$, and we know $\theta$ and $a$, then $x = a\times\tan\theta$; if we know $x$ and $a$, then $\theta=\tan^{-1}(\frac{x}{a})$.