Question

What is the value of x to the nearest tenth??

Answer 1

Answer:

$\displaystyle 12,3 ≈ x$

Step-by-step explanation:

We have to determine which trigonometric ratio to use, depending on what is displayed for us, and we will be using the cotangent [or tangent] ratio, this time with two angle measures:

$\displaystyle cot\:39° = \frac{x}{10} → 10cot\:39° ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:39° = \frac{10}{x} → \frac{10}{tan\:39°} ≈ 12,34897157 ≈ 12,3 \\ \\ \\ OR \\ \\ \\ cot\:51° = \frac{10}{x} → \frac{10}{cot\:51°} ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:51° = \frac{x}{10} → 10tan\:51° ≈ 12,34897157 ≈ 12,3$

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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