Question

fall 2025 geometry b wwva trigonometric ratios what are the values of the three trigonometric ratios for angle l, in simplest form? sin(l)= cos(l)= 3/5 3/4 tan(l)= 4/5 5/4

Explanation:

Step1: Recall sine ratio formula

$\sin(L)=\frac{\text{opposite}}{\text{hypotenuse}}$
For angle $L$, the opposite side is $MN = 20$ and the hypotenuse is $LN=25$. So $\sin(L)=\frac{20}{25}=\frac{4}{5}$.

Step2: Recall cosine ratio formula

$\cos(L)=\frac{\text{adjacent}}{\text{hypotenuse}}$
For angle $L$, the adjacent side is $ML = 15$ and the hypotenuse is $LN = 25$. So $\cos(L)=\frac{15}{25}=\frac{3}{5}$.

Step3: Recall tangent ratio formula

$\tan(L)=\frac{\text{opposite}}{\text{adjacent}}$
For angle $L$, the opposite side is $MN = 20$ and the adjacent side is $ML=15$. So $\tan(L)=\frac{20}{15}=\frac{4}{3}$.

Answer:

$\sin(L)=\frac{4}{5}$, $\cos(L)=\frac{3}{5}$, $\tan(L)=\frac{4}{3}$