Question

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

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 28\) and \(b=45\). So \(c=\sqrt{28^{2}+45^{2}}=\sqrt{784 + 2025}=\sqrt{2809}=53\).

Step2: Calculate sine of ∠R

Sine is opposite - over - hypotenuse. Opposite side to ∠R is 45 and hypotenuse is 53. So \(\sin(R)=\frac{45}{53}\).

Step3: Calculate cosine of ∠R

Cosine is adjacent - over - hypotenuse. Adjacent side to ∠R is 28 and hypotenuse is 53. So \(\cos(R)=\frac{28}{53}\).

Step4: Calculate tangent of ∠R

Tangent is opposite - over - adjacent. Opposite side to ∠R is 45 and adjacent side is 28. So \(\tan(R)=\frac{45}{28}\).

Answer:

\(\sin(R)=\frac{45}{53}\)
\(\cos(R)=\frac{28}{53}\)
\(\tan(R)=\frac{45}{28}\)