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kvasek [131]
2 years ago
8

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.)
Mathematics
1 answer:
WINSTONCH [101]2 years ago
4 0

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 <u>40</u>,

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}

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