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

15.36.

p/r.

Explanation:

cos 43 = c/21

c = 21 cos 43

c = 15.36.

Tan P = opposite side / adjacent side

= p/r.

Answer 2

2. a.
`\displaystyle (p)/(r)`

1.
`\displaystyle 15,35842773 ≈ c`

Step-by-step explanation:

2. Extended Information on Trigonometric Ratios

`\displaystyle (OPPOSITE)/(HYPOTENUSE) = sin\:θ \\ (ADJACENT)/(HYPOTENUSE) = cos\:θ \\ (OPPOSITE)/(ADJACENT) = tan\:θ \\ (HYPOTENUSE)/(ADJACENT) = sec\:θ \\ (HYPOTENUSE)/(OPPOSITE) = csc\:θ \\ (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° = (21)/(c) → (21)/(sec\:43°) ≈ c → 15,35842773 ≈ c \\ \\ OR \\ \\ cos\:43° = (c)/(21) → 21cos\:43° ≈ c → 15,35842773 ≈ c`

ONCE AGAIN...

Extended Information on Trigonometric Ratios

`\displaystyle (OPPOSITE)/(HYPOTENUSE) = sin\:θ \\ (ADJACENT)/(HYPOTENUSE) = cos\:θ \\ (OPPOSITE)/(ADJACENT) = tan\:θ \\ (HYPOTENUSE)/(ADJACENT) = sec\:θ \\ (HYPOTENUSE)/(OPPOSITE) = csc\:θ \\ (ADJACENT)/(OPPOSITE) = cot\:θ`

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