In a right triangle the side opposite the 30 degree angle is 5 meters.Find the adjacent side.
please don't switch names ...
As I pointed out in the other posts
the ratio of sides of a 30-60-90 triangle is 1:√3:2
so if the opposite side is 5, the adjacent side is 5√3
To find the adjacent side of a right triangle, we can use trigonometric ratios. In this case, since we are given the angle of 30 degrees and the opposite side, we can use the trigonometric ratio of tangent.
Tangent (tan) of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, by rearranging the formula, we can solve for the adjacent side.
In this case, tan(30 degrees) = opposite side / adjacent side.
Substituting the given values, we have:
tan(30 degrees) = 5 / adjacent side.
The tangent of 30 degrees is equal to (√3) / 3. So we can rewrite the equation as:
(√3) / 3 = 5 / adjacent side.
To solve for the adjacent side, we can cross-multiply and then divide:
(√3) * adjacent side = 3 * 5.
adjacent side = (3 * 5) / (√3).
Simplifying this expression, we have:
adjacent side = 15 / (√3).
To rationalize the denominator (√3), we multiply the numerator and denominator by (√3):
adjacent side = (15 * √3) / (√3 * √3).
adjacent side = (15 * √3) / 3.
Simplifying this expression gives us the final answer:
adjacent side = 5√3 meters.