CPM Homework Help : CCG Problem 5-17

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5-17.

For each triangle below, write an equation relating the reference angle (the given acute angle) with the two side lengths of the right triangle. Then solve your equation for $x$ .

Hint:

Refer to the Math Notes box in Lesson 5.1.2 if you need help writing an equation relating to a reference angle.
It will be helpful for all three parts of this problem.

Step 1(a):
$\sin\theta=\frac{\text{opp}}{\text{hyp}}$
Step 2(a):
$\text{sin}(22^{\circ}) = \frac{\it{x}}{17}$
Step 3(a):
$17\text{ sin}(22^\circ) = \it{x}$
Answer (a):
$x \approx 6.37$

Step 1(b):

$\text{tan}\theta = \frac{\text{opp}}{\text{adj}}$

Step 2(b):

$\text{tan}(49º) = \frac{7}{\textit{x}}$

Step 3(b):

$x\text{ tan}(49º) = 7$

Step 4(b):

$\frac{x\tan(49º)}{\tan(49º)}=\frac{7}{\tan(49º)}$

Step 5(b):

$x = \frac{7}{\text{tan}(49^\circ)}$

Answer (b):

$x \approx 6.09$

Hint (c):
Follow the same steps as in parts (a) and (b).