Answer:
cos B = [tex]\frac{7}{25}[/tex]
tan B = [tex]\frac{24}{7}[/tex]
sin B = [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
In the right triangle, there are three sides and 2 acute angles
- Hypotenuse ⇒ the opposite side of the right angle
- Leg1 and Leg 2 ⇒ the sides of the right angle
The trigonometry functions of one of the acute angles Ф are
- sin Ф = opposite leg/hypotenuse
- cos Ф = adjacent leg/hypotenuse
- tan Ф = opposite leg/adjacent leg
In Δ ACB
∵ ∠C is the right angle
∴ AB is the hypotenuse
∵ AC is the opposite side of ∠B ⇒ leg1
∵ CB is the adjacent side of ∠B ⇒ leg2
→ By using the ratios above
∴ cos B = [tex]\frac{CB}{AB}[/tex] , tan B = [tex]\frac{AC}{CB}[/tex] , sin B = [tex]\frac{AC}{AB}[/tex]
∵ CB = 7, AB = 25, AC = 24
∴ cos B = [tex]\frac{7}{25}[/tex]
∴ tan B = [tex]\frac{24}{7}[/tex]
∴ sin B = [tex]\frac{24}{25}[/tex]
