Question

find the sine, cosine, and tangent of ∠s.
t

5

s

12

u

simplify your answers and write them as proper fractions, improper fractions, or whole numbers.
sin(s) =
cos(s) =
tan(s) =

Explanation:

Step1: Find the hypotenuse SU

In right triangle \( STU \), by Pythagorean theorem \( SU = \sqrt{ST^2 + TU^2} \). Given \( ST = 5 \), \( TU = 12 \), so \( SU=\sqrt{5^2 + 12^2}=\sqrt{25 + 144}=\sqrt{169} = 13 \).

Step2: Calculate \( \sin(S) \)

\( \sin(S)=\frac{\text{opposite to } S}{\text{hypotenuse}}=\frac{TU}{SU}=\frac{12}{13} \)

Step3: Calculate \( \cos(S) \)

\( \cos(S)=\frac{\text{adjacent to } S}{\text{hypotenuse}}=\frac{ST}{SU}=\frac{5}{13} \)

Step4: Calculate \( \tan(S) \)

\( \tan(S)=\frac{\text{opposite to } S}{\text{adjacent to } S}=\frac{TU}{ST}=\frac{12}{5} \)

Answer:

\( \sin(S)=\frac{12}{13} \)
\( \cos(S)=\frac{5}{13} \)
\( \tan(S)=\frac{12}{5} \)