Question

find the sine, cosine, and tangent of ∠q. simplify your answers and write them as proper fraction numbers. sin(q) = cos(q) = tan(q) =

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 39$ and $b = 80$. So $c=\sqrt{39^{2}+80^{2}}=\sqrt{1521 + 6400}=\sqrt{7921}=89$.

Step2: Calculate sine of ∠Q

The sine of an angle in a right - triangle is defined as $\sin(Q)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the opposite side to ∠Q is $39$ and the hypotenuse is $89$. So $\sin(Q)=\frac{39}{89}$.

Step3: Calculate cosine of ∠Q

The cosine of an angle in a right - triangle is defined as $\cos(Q)=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to ∠Q is $80$ and the hypotenuse is $89$. So $\cos(Q)=\frac{80}{89}$.

Step4: Calculate tangent of ∠Q

The tangent of an angle in a right - triangle is defined as $\tan(Q)=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to ∠Q is $39$ and the adjacent side is $80$. So $\tan(Q)=\frac{39}{80}$.

Answer:

$\sin(Q)=\frac{39}{89}$
$\cos(Q)=\frac{80}{89}$
$\tan(Q)=\frac{39}{80}$