Find x 58 degrees and adjacent 4.0

1 answer:

4 0

A special kind of triangle is a right triangle whose definite characteristic is having a 90° angle. It is also special because there are derived trigonometric formulas/identities that can be applied to it. A right triangle has three sides: hypotenuse, adjacent side and opposite side. The hypotenuse is the longest side of the right triangle. You can determine this visually, if not, quantitatively. The other sides are with respect to a given angle.

For the problem, it might have asked for the opposite side or the hypotenuse. We use the cosine function to find the hypotenuse:

cos 58° = adjacent/hypotenuse = 4/hypotenuse
hypotenuse = 7.55 units

Then, we use the tangent function to find the opposite side.

tan 58° = opposite/adjacent = opposite/4
opposite = 6.4 units

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Use both. This works because either way, they will lie on the same line with the same slope. So, starting at (-5,-3), go down two points (-)* and to the left 1 (+)*, then, starting at (-5,-3) again, go up two points (+)* then to the right 1 point (-)*.

* If the number is negative, you either go down or to the right. If the number is positive, you go up and to the left.

**Rise over run refers to the change in the y-axis and the change in the x-axis: $\frac{rise}{run} =\frac{y-axis}{x-axis}$ . Only one number is negative because, if both were negative, that would make a positive number, but the slope is -2, not 2.