Question

find the sine, cosine, and tangent of $\angle t$. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. $\sin(t) = \square$ $\cos(t) = \square$ $\tan(t) = \square$

Explanation:

Step1: Find hypotenuse $RT$

Use Pythagorean theorem:
$$RT = \sqrt{RS^2 + ST^2} = \sqrt{45^2 + 28^2} = \sqrt{2025 + 784} = \sqrt{2809} = 53$$

Step2: Calculate $\sin(T)$

Opposite over hypotenuse:
$$\sin(T) = \frac{RS}{RT} = \frac{45}{53}$$

Step3: Calculate $\cos(T)$

Adjacent over hypotenuse:
$$\cos(T) = \frac{ST}{RT} = \frac{28}{53}$$

Step4: Calculate $\tan(T)$

Opposite over adjacent:
$$\tan(T) = \frac{RS}{ST} = \frac{45}{28}$$

Answer:

$\sin(T) = \frac{45}{53}$
$\cos(T) = \frac{28}{53}$
$\tan(T) = \frac{45}{28}$