Question

What is the value of x to the nearest degree?

Answer 1

Answer:

Step-by-step 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

Answer:

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:

$\displaystyle cot^{-1}\: \frac{5}{8} ≈ 57,99461679° ≈ 58° \\ \\ OR \\ \\ tan{-1}\: 1\frac{3}{5} ≈ 57,99461679° ≈ 58°$

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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