Question

What is the value of x to the nearest degree?

Answer 1

Explanation:

This is right triangle trig. The side opposite the x is 8, and the side adjacent to the x is 5. The tangent ratio uses those sides. We need to find what angle has a tangent of 8/5. To do this, make sure your calculator is in degree mode. Then hit "2nd" then tan and you will see tan with a little -1 and a parenthesis. Enter 8/5 and hit "enter" and you will get an angle measure of 57.9946. Rounded to the nearest degree this is 58 degrees. That's your answer!

Answer 2

b
`\displaystyle 58`

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, however, since we are solving for an angle measure, we must use the inverse:

`\displaystyle cot^(-1)\: (5)/(8) ≈ 57,99461679° ≈ 58° \\ \\ OR \\ \\ tan{-1}\: 1(3)/(5) ≈ 57,99461679° ≈ 58°`

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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