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: Find the adjacent side to ∠H

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let the adjacent side to ∠H be \(x\). We know \(c = 74\) and \(b = 24\). Then \(x=\sqrt{74^{2}-24^{2}}=\sqrt{(74 + 24)(74 - 24)}=\sqrt{98\times50}=\sqrt{4900}=70\).

Step2: Calculate sin(H)

By the definition of sine in a right - triangle \(\sin(H)=\frac{\text{opposite}}{\text{hypotenuse}}\). The opposite side to ∠H is 24 and the hypotenuse is 74. So \(\sin(H)=\frac{24}{74}=\frac{12}{37}\).

Step3: Calculate cos(H)

By the definition of cosine in a right - triangle \(\cos(H)=\frac{\text{adjacent}}{\text{hypotenuse}}\). The adjacent side to ∠H is 70 and the hypotenuse is 74. So \(\cos(H)=\frac{70}{74}=\frac{35}{37}\).

Step4: Calculate tan(H)

By the definition of tangent in a right - triangle \(\tan(H)=\frac{\text{opposite}}{\text{adjacent}}\). The opposite side to ∠H is 24 and the adjacent side is 70. So \(\tan(H)=\frac{24}{70}=\frac{12}{35}\).

Answer:

\(\sin(H)=\frac{12}{37}\), \(\cos(H)=\frac{35}{37}\), \(\tan(H)=\frac{12}{35}\)