Respuesta :
Answer: b = 40
sin B = [tex]\frac{40}{41}[/tex]
cos B = [tex]\frac{9}{41}[/tex]
tg B = [tex]\frac{40}{9}[/tex]
sec B = [tex]\frac{41}{9}[/tex]
csc B = [tex]\frac{41}{40}[/tex]
cot B = [tex]\frac{9}{40}[/tex]
Step-by-step explanation: If the right angle is at C, then the hypothenuse is side c = 41.
Using Pythagorean Theorem:
hypotenuse² = side² + side²
41² = 9² + b²
b = [tex]\sqrt{1681 - 81}[/tex]
b = 40
The side b length is 40,
The trigonometric functions of a right triangle are:
1) Sine = [tex]\frac{opposite side}{hypotenuse}[/tex]
sin (B) = [tex]\frac{b}{c}[/tex]
Sin(B) = [tex]\frac{40}{41}[/tex]
2) Cosine = [tex]\frac{adjacent side}{hypotenuse}[/tex]
cos (B) = [tex]\frac{a}{c}[/tex]
cos (B) = [tex]\frac{9}{41}[/tex]
3) Tangent = [tex]\frac{opposite}{adjacent}[/tex]
tg (B) = [tex]\frac{b}{a}[/tex]
tg (B) = [tex]\frac{40}{9}[/tex]
4) Sec = [tex]\frac{1}{cos}[/tex]
sec(B) = [tex]\frac{c}{a}[/tex]
sec(B) = [tex]\frac{41}{9}[/tex]
5) Cosecant = [tex]\frac{1}{sin}[/tex]
csc(B) = [tex]\frac{c}{b}[/tex]
csc(B) = [tex]\frac{41}{40}[/tex]
6) Cotangent = [tex]\frac{1}{tg}[/tex]
cot(B) = [tex]\frac{a}{b}[/tex]
cot(B) = [tex]\frac{9}{40}[/tex]
