Question

write the ratios for sin m, cos m, and tan m. give the exact value and a four - decimal approximation.

sin m=
(type an exact answer in simplified form. type an integer or a fraction.)

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 $\angle M$, the opposite side to $\angle M$ is $KL = 52$, the adjacent side to $\angle M$ is $KM=165$, and the hypotenuse is $LM = 173$.

Step2: Calculate $\sin M$

$\sin M=\frac{KL}{LM}=\frac{52}{173}$
The four - decimal approximation: $\sin M\approx0.3006$

Step3: Calculate $\cos M$

$\cos M=\frac{KM}{LM}=\frac{165}{173}$
The four - decimal approximation: $\cos M\approx0.9538$

Step4: Calculate $\tan M$

$\tan M=\frac{KL}{KM}=\frac{52}{165}$
The four - decimal approximation: $\tan M\approx0.3152$

Answer:

$\sin M=\frac{52}{173}\approx0.3006$, $\cos M=\frac{165}{173}\approx0.9538$, $\tan M=\frac{52}{165}\approx0.3152$