Sin cos tan

In right triangle ABC with a right angle at B, the sides are |AB| = 7 cm, |BC| = 5 cm, and |AC| = 8.6 cm. Find to two decimal places:
A. sin C
B. cos C
C. tan C

Final Answer:

S =  0.814
K =  0.5814
T =  1.4

Step-by-step explanation:

$$\begin{gathered} c=7\text{cm} \\ a=5\text{cm} \\ b=8.6\text{cm} \\ B=90{}^{\circ } \\ S=\sin C=c:b \\ S=\frac{c}{b}=\frac{7}{8.6}=\frac{35}{43}=0.814 \end{gathered}$$

$$\begin{gathered} K=\cos C=a:b \\ K=\frac{a}{b}=\frac{5}{8.6}=\frac{25}{43}=0.5814 \end{gathered}$$

$$\begin{gathered} T=\tan C=c:a=\frac{\sin C}{\cos C} \\ T=\frac{c}{a}=\frac{7}{5}=1\frac{2}{5}=1.4 \\ \text{ Verifying Solution: } \\ {b}_2=\sqrt{a^2+c^2}=\sqrt{5^2+7^2}=\sqrt{74}\text{cm}\doteq 8.6023\text{cm} \end{gathered}$$

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