Question

problem 1
solve for x. round your answers to the nearest hundredths

problem 2
solve for x. round your answers to the nearest hundredths

Explanation:

Problem 1

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=29^\circ$, opposite side $=7$, adjacent side $=x$.
$\tan(29^\circ) = \frac{7}{x}$

Step2: Rearrange to solve for x

$x = \frac{7}{\tan(29^\circ)}$

Step3: Calculate value

$\tan(29^\circ) \approx 0.5543$, so $x \approx \frac{7}{0.5543} \approx 12.63$

Problem 2

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\theta=54^\circ$, opposite side $=22$, hypotenuse $=x$.
$\sin(54^\circ) = \frac{22}{x}$

Step2: Rearrange to solve for x

$x = \frac{22}{\sin(54^\circ)}$

Step3: Calculate value

$\sin(54^\circ) \approx 0.8090$, so $x \approx \frac{22}{0.8090} \approx 27.19$

Answer:

Problem 1: $x \approx 12.63$
Problem 2: $x \approx 27.19$