Question

find the sine, cosine, and tangent of ∠g.

write your answer in simplified, rationalized form. do not round.

sin(g) =
cos(g) =
tan(g) =

Explanation:

Step1: Find hypotenuse $HG$

Use Pythagorean theorem:
$$HG = \sqrt{HF^2 + FG^2} = \sqrt{5^2 + 7^2} = \sqrt{25+49} = \sqrt{74}$$

Step2: Calculate $\sin(G)$

Opposite over hypotenuse:
$$\sin(G) = \frac{HF}{HG} = \frac{5}{\sqrt{74}} = \frac{5\sqrt{74}}{74}$$

Step3: Calculate $\cos(G)$

Adjacent over hypotenuse:
$$\cos(G) = \frac{FG}{HG} = \frac{7}{\sqrt{74}} = \frac{7\sqrt{74}}{74}$$

Step4: Calculate $\tan(G)$

Opposite over adjacent:
$$\tan(G) = \frac{HF}{FG} = \frac{5}{7}$$

Answer:

$\sin(G) = \frac{5\sqrt{74}}{74}$
$\cos(G) = \frac{7\sqrt{74}}{74}$
$\tan(G) = \frac{5}{7}$