Question

find the sine, cosine, and tangent of ∠h. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. sin(h) = cos(h) = tan(h) =

Explanation:

Step1: Calculate hypotenuse $FH$

Use Pythagorean theorem:
$$FH = \sqrt{FG^2 + GH^2} = \sqrt{45^2 + 28^2} = \sqrt{2025 + 784} = \sqrt{2809} = 53$$

Step2: Find $\sin(H)$

Opposite over hypotenuse:
$$\sin(H) = \frac{FG}{FH} = \frac{45}{53}$$

Step3: Find $\cos(H)$

Adjacent over hypotenuse:
$$\cos(H) = \frac{GH}{FH} = \frac{28}{53}$$

Step4: Find $\tan(H)$

Opposite over adjacent:
$$\tan(H) = \frac{FG}{GH} = \frac{45}{28}$$

Answer:

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