Question

Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and
then find the values of the six trigonometric functions for angle B.

a = 9, C = 41

The unknown side length bis

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer 1

Answer: b = 40

sin B = $\frac{40}{41}$

cos B = $\frac{9}{41}$

tg B = $\frac{40}{9}$

sec B = $\frac{41}{9}$

csc B = $\frac{41}{40}$

cot B = $\frac{9}{40}$

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 = $\sqrt{1681 - 81}$

b = 40

The side b length is 40,

The trigonometric functions of a right triangle are:

1) Sine = $\frac{opposite side}{hypotenuse}$

sin (B) = $\frac{b}{c}$

Sin(B) = $\frac{40}{41}$

2) Cosine = $\frac{adjacent side}{hypotenuse}$

cos (B) = $\frac{a}{c}$

cos (B) = $\frac{9}{41}$

3) Tangent = $\frac{opposite}{adjacent}$

tg (B) = $\frac{b}{a}$

tg (B) = $\frac{40}{9}$

4) Sec = $\frac{1}{cos}$

sec(B) = $\frac{c}{a}$

sec(B) = $\frac{41}{9}$

5) Cosecant = $\frac{1}{sin}$

csc(B) = $\frac{c}{b}$

csc(B) = $\frac{41}{40}$

6) Cotangent = $\frac{1}{tg}$

cot(B) = $\frac{a}{b}$

cot(B) = $\frac{9}{40}$