Question

What is the value of x to the nearest tenth?

Answer 1

`\displaystyle 1,6 ≈ 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\:37° = (2,1)/(x) → (2,1)/(cot\:37°) ≈ 1,582463505 ≈ 1,6 \\ \\ OR \\ \\ tan\:37° = (x)/(2,1) → 2,1tan\:37° ≈ 1,582463505 ≈ 1,6`

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`

I am joyous to assist you anytime.

Answer 2

You need to use some trig... but I will try to explain it as best as possible. If you imagine a unit circle, we describe the coordinate points that line on the circle in terms of cosine and sine. A certain coordinate point on the circle can be written like (cos(x),sin(x)). "X" is going to be the angle from the center of the circle starting at point (1,0). Now imagine this triangle being fitted into a circle. The leg represents the x and y length that lead up to a point on the circle. The hypotenuse of the triangle represents the radius of the circle.

We need to find the hypotenuse first.

cos(37 degrees) x hypotenuse = 2.1

hypotenuse = 2.63 approx.

So the "x" length or the sine length is...

sin(37 degrees) x 2.63 = 1.6 approx.

answer: 1.6