Question

find the missing side. round to the nearest tenth.
17)
a) 13.4
b) 14.1
c) 11.5
d) 10.5
○ a a
○ b b
○ c c
○ d d

Explanation:

Step1: Identify trigonometric ratio

For the $73^\circ$ angle, $x$ is the adjacent side, and 11 is the hypotenuse. Use cosine:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(73^\circ) = \frac{x}{11}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = 11 \times \cos(73^\circ)$
Calculate $\cos(73^\circ) \approx 0.2924$, so:
$x \approx 11 \times 0.2924 = 3.2164$
*Correction: Re-identify sides: $x$ is adjacent to $73^\circ$, hypotenuse=11. Wait, no—wait, $73^\circ$ is at the top left, right angle at top right. So $x$ is adjacent to $73^\circ$, hypotenuse=11. Wait, no, error: $\cos(73^\circ) = \frac{x}{11}$ → $x=11\cos73\approx3.2$ is not an option. Re-assess: $x$ is opposite to $73^\circ$? No, right angle at top right: the angle $73^\circ$ has adjacent side $x$, opposite side is the bottom left side, hypotenuse=11. Wait, no—wait, sine: $\sin(73^\circ)=\frac{x}{11}$? No, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. If $73^\circ$ is at top left, opposite side is $x$. Yes! That's the mistake. Correct:
$\sin(73^\circ) = \frac{x}{11}$
$x = 11 \times \sin(73^\circ)$
$\sin(73^\circ)\approx0.9563$
$x\approx11\times0.9563=10.5193$

Step4: Round to nearest tenth

$x\approx10.5$

Answer:

D) 10.5