Question

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

Answer 1

`\displaystyle 12,3 ≈ x`

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° = (x)/(10) → 10cot\:39° ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:39° = (10)/(x) → (10)/(tan\:39°) ≈ 12,34897157 ≈ 12,3 \\ \\ \\ OR \\ \\ \\ cot\:51° = (10)/(x) → (10)/(cot\:51°) ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:51° = (x)/(10) → 10tan\:51° ≈ 12,34897157 ≈ 12,3`

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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