Question

what are the values of the three trigonometric ratios for angle l, in simplest form? sin(l) = cos(l) = tan(l) =

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ for an acute angle $\theta$. For angle $L$, the opposite side to angle $L$ is $MN = 20$, the adjacent side to angle $L$ is $LM=15$, and the hypotenuse is $LN = 25$.

Step2: Calculate $\sin(L)$

$\sin(L)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{20}{25}=\frac{4}{5}$

Step3: Calculate $\cos(L)$

$\cos(L)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{15}{25}=\frac{3}{5}$

Step4: Calculate $\tan(L)$

$\tan(L)=\frac{\text{opposite}}{\text{adjacent}}=\frac{20}{15}=\frac{4}{3}$

Answer:

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