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.)
1 answer:
Answer: b = 40
sin B = ![\frac{40}{41}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B41%7D)
cos B = ![\frac{9}{41}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B41%7D)
tg B = ![\frac{40}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B9%7D)
sec B = ![\frac{41}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B41%7D%7B9%7D)
csc B = ![\frac{41}{40}](https://tex.z-dn.net/?f=%5Cfrac%7B41%7D%7B40%7D)
cot B = ![\frac{9}{40}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B40%7D)
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}](https://tex.z-dn.net/?f=%5Csqrt%7B1681%20-%2081%7D)
b = 40
The side b length is <u>40</u>,
The trigonometric functions of a right triangle are:
1) Sine =
sin (B) = ![\frac{b}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bc%7D)
Sin(B) = ![\frac{40}{41}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B41%7D)
2) Cosine =
cos (B) = ![\frac{a}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bc%7D)
cos (B) = ![\frac{9}{41}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B41%7D)
3) Tangent = ![\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Badjacent%7D)
tg (B) = ![\frac{b}{a}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba%7D)
tg (B) = ![\frac{40}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B9%7D)
4) Sec = ![\frac{1}{cos}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bcos%7D)
sec(B) = ![\frac{c}{a}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Ba%7D)
sec(B) = ![\frac{41}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B41%7D%7B9%7D)
5) Cosecant = ![\frac{1}{sin}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bsin%7D)
csc(B) = ![\frac{c}{b}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bb%7D)
csc(B) = ![\frac{41}{40}](https://tex.z-dn.net/?f=%5Cfrac%7B41%7D%7B40%7D)
6) Cotangent = ![\frac{1}{tg}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Btg%7D)
cot(B) = ![\frac{a}{b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D)
cot(B) = ![\frac{9}{40}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B40%7D)
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