Question

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

Explanation:

Step1: Find the length of the hypotenuse \(HG\)

By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 10\), \(b=24\) and \(c = HG\).

$$HG=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26$$

Step2: Calculate \(\sin(H)\)

\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle H\), the opposite side to \(\angle H\) is \(IG = 24\) and the hypotenuse \(HG=26\)
\(\sin(H)=\frac{24}{26}=\frac{12}{13}\)

Step3: Calculate \(\cos(H)\)

\(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle H\), the adjacent side to \(\angle H\) is \(HI = 10\) and the hypotenuse \(HG = 26\)
\(\cos(H)=\frac{10}{26}=\frac{5}{13}\)

Step4: Calculate \(\tan(H)\)

\(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle H\), the opposite side to \(\angle H\) is \(IG = 24\) and the adjacent side to \(\angle H\) is \(HI=10\)
\(\tan(H)=\frac{24}{10}=\frac{12}{5}\)

Answer:

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