If the side opposite a 60-degree angle in a 30-60-90 right triangle is
7
3
–
√
cm
long, how long is the hypotenuse?(1 point)
In a 30-60-90 right triangle, the ratio of the side opposite the 30-degree angle to the hypotenuse is 1:2, and the ratio of the side opposite the 60-degree angle to the hypotenuse is √3:2.
Given that the side opposite the 60-degree angle is –√7 cm long, we can set up the following equation:
√3/hypotenuse = –√7/2
To solve for the hypotenuse, we can cross-multiply:
hypotenuse*√3 = 2*(-√7)
hypotenuse = (2*(-√7))/√3
hypotenuse = -2(√7/√3)
Since we can't have a negative length, we discard the negative sign:
hypotenuse = 2(√7/√3)
Simplifying further:
hypotenuse = 2(√21/√9)
Since √9 = 3, we can simplify again:
hypotenuse = 2(√21/3)
Therefore, the length of the hypotenuse is 2(√21/3) cm.