Question

triangle 5
adjacent side 52
opposite side 30
hypotenuse 60
theta

Explanation:

Step1: Identify the trigonometric ratio

We can use the sine, cosine, or tangent function. Let's use the sine function, where $\sin(\theta)=\frac{\text{Opposite}}{\text{Hypotenuse}}$. The opposite side is 30 and the hypotenuse is 60.
$\sin(\theta)=\frac{30}{60}$

Step2: Simplify the ratio

$\frac{30}{60}=\frac{1}{2}$

Step3: Find the angle whose sine is $\frac{1}{2}$

We know that $\sin(30^\circ)=\frac{1}{2}$, so $\theta = 30^\circ$. We can also verify with cosine: $\cos(\theta)=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{52}{60}\approx0.8667$, and $\cos(30^\circ)=\frac{\sqrt{3}}{2}\approx0.8660$, which is close (considering possible rounding in the given side lengths). Or with tangent: $\tan(\theta)=\frac{\text{Opposite}}{\text{Adjacent}}=\frac{30}{52}\approx0.5769$, and $\tan(30^\circ)=\frac{1}{\sqrt{3}}\approx0.5774$, also close. So the angle $\theta$ is approximately $30^\circ$.

Answer:

$\boldsymbol{30^\circ}$ (or approximately, considering the side lengths, it's very close to $30^\circ$)