Exercise 18 Page 573

Start by identifying the hypotenuse of the right triangle. Then find the sides that are opposite and adjacent to each angle.

Ratios for ∠ J: sin J=4/5=0.80, cos J = 3/5=0.60, tan J=4/3≈ 1.33

Ratios for ∠ L: sin L=3/5=0.60, cos L = 4/5=0.80, tan L=3/4≈ 0.75

Practice makes perfect

For the given right triangle, we want to write the ratios for the sine, cosine, and tangent of ∠ J and ∠ L.

Ratios for ∠ J

Let's start by identifying the hypotenuse of the triangle and the sides that are opposite and adjacent to ∠ J.

We see that the length of the hypotenuse is 5. The length of the side adjacent to ∠ J is 3 and the length of the side opposite to ∠ J is 4. With this information, we can find the desired ratios.

Ratio	Definition	Value
sin J	Length of leg opposite to∠ J/Length of hypotenuse	4/5=0.80
cos J	Length of leg adjacent to∠ J/Length of hypotenuse	3/5= 0.60
tan J	Length of leg opposite to∠ J/Length of leg adjacent to∠ J	4/3≈ 1.33

Ratios for ∠ L

We already know the length of the hypotenuse is 5. Let's identify the sides that are opposite and adjacent to ∠ L.

The length of the side adjacent to ∠ L is 4 and the length of the side opposite to ∠ L is 3. With this information, we can find the desired ratios.

Ratio	Definition	Value
sin L	Length of leg opposite to∠ L/Length of hypotenuse	3/5=0.60
cos L	Length of leg adjacent to∠ L/Length of hypotenuse	4/5=0.80
tan L	Length of leg opposite to∠ L/Length of leg adjacent to∠ L	3/4=0.75

Subchapter links

Check Your Understanding p.573

Practice and Problem Solving p.573-576

H.O.T. Problems p.576

Standardized Test Practice p.577

Spiral Review p.577

Skills Review p.577

Exercise 18 Page 573

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Ratios for ∠ J

Ratios for ∠ L