Question

8-2: practice & problem-solving day 1
part 1 of 6
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.)
due
feb 12-12.00 am

Explanation:

Step1: Recall sine definition

For angle $M$, $\sin M = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\sin M$

Opposite side to $M$ is $KL = 4\sqrt{3}$, hypotenuse $ML = 8$.
$\sin M = \frac{4\sqrt{3}}{8}$

Step3: Simplify the fraction

Cancel common factor 4:
$\sin M = \frac{\sqrt{3}}{2}$

Step4: Calculate decimal approximation

$\frac{\sqrt{3}}{2} \approx \frac{1.73205}{2} = 0.8661$

Answer:

Exact value: $\frac{\sqrt{3}}{2}$
Four-decimal approximation: $0.8661$