Question

finding the values of trigonometric ratios
what are the values of the three trigonometric ratios for angle l, in simplest form?
sin(l) =
cos(l) =
tan(l) =
(the triangle has right angle at m, side mn = 20, ml = 15, nl = 25)

Explanation:

Step1: Identify sides for angle L

For $\angle L$:

• Opposite side: $MN = 20$
• Adjacent side: $LM = 15$
• Hypotenuse: $LN = 25$

Step2: Calculate $\sin(L)$

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

Step3: Calculate $\cos(L)$

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

Step4: Calculate $\tan(L)$

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

Answer:

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