Let x be the side opposite the 30° angle and y be the side opposite the 60° angle.
In a 30°-60°-90° triangle, the side lengths are in the ratio 1:√3:2, where the smallest side opposite the 30° angle is 1, the side opposite the 60° angle is √3, and the hypotenuse (the side opposite the 90° angle) is 2.
Since the given hypotenuse is 6, we can set up the proportion 2/6. This means the ratio of the sides of this triangle is also 1:(√3):3. Hence, the side lengths are:
x = 6/2 = 3 (since x is opposite the 30° angle)
y = 3√3 (since y is opposite the 60° angle)
Thus, x = 3 and y = 3√3 in simplest radical form.
Find the length of x and y in the 30°-60°-90° triangle. Leave answer in simplest radical form.
hypotenuse: 6
angle: 60°
show work.
1 answer