Consider a triangle ABC right-angled at B in which the side BC = 9 and the angle α = 30° (α being the angle \(\widehat{ABC}\)).
Using these information, can you calculate the lenghts AB and AC?
Of course I am! (just kidding...)
"The world won't be destroyed by those who do evil, but by those who watch them without doing anything."
Albert Einstein
it is a 30 60 90 triangle: x,x sqrt(3),2x
60 is the opossite of 9 (x sqrt(3))
9/sqrt(3) = 5.1961524227066319 or 3sqrt(3) is opposite of 30 (x)
6sqrt(3) the opposite of 90 (2x)
Hint:
Pythagorus's theorem:
“In any triangle right-angled at B, the lenght of the hypotenuse squared is equal to the sum of the squares of the lenghts of the two other sides” or, in other words:
AC²=AB²+BC²
Trigonometric functions:
In a right triangle, for any non-right angle α:
\(\sin(\alpha)=\frac{\text{opposite side}}{\text{hypotenuse}} \\\cos(\alpha)=\frac{\text{adjacent side}}{\text{hypotenuse}} \\\tan(\alpha)=\frac{\text{opposite side}}{\text{adjacent side}}\)
Respectively the sinus, the cosinus and the tangent of α.