Question

1. In the triangle below, determine the value of c.

2. In the triangle below, what ratio is tan P?

a. p/r

b. r/q

c. r/p

d. p/q

Answer 1

Answer:

2. a. $\displaystyle \frac{p}{r}$

1. $\displaystyle 15,35842773 ≈ c$

Step-by-step explanation:

2. Extended Information on Trigonometric Ratios

$\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ$

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1. We have to determine which trigonometric ratio[s] to use, depending on what is given to us, and in this case, we will be using the secant [or cosine] ratio:

$\displaystyle sec\:43° = \frac{21}{c} → \frac{21}{sec\:43°} ≈ c → 15,35842773 ≈ c \\ \\ OR \\ \\ cos\:43° = \frac{c}{21} → 21cos\:43° ≈ c → 15,35842773 ≈ c$

ONCE AGAIN...

Extended Information on Trigonometric Ratios

$\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ$

I am joyous to assist you anytime.

Answer 2

Answer:

15.36.

p/r.

Step-by-step explanation:

cos 43 = c/21

c = 21 cos 43

c = 15.36.

Tan P = opposite side / adjacent side

=  p/r.