Question

Given a right-angled triangle with angles measuring 30°, 60°, and 90°, and the side opposite the 60° angle is 10 cm, find the length (n) of the side opposite the 30° angle. Write your answer in the simplest radical form.

a. 10/√3
b. 10√3/3
c. 10/3
d. 10√3

Answer 1

The length (n) of the side opposite the 30° angle in a right-angled triangle, with the side opposite the 60° angle being 10 cm, is 5 cm.

Step-by-step explanation:

The student asked for the length of the side opposite the 30° angle in a right-angled triangle where the side opposite the 60° angle is 10 cm. Using the properties of 30°-60°-90° triangles, we know that the side opposite the 30° angle (n) is half the hypotenuse. In this case, if the side opposite the 60° is 10 cm, this side is the longer leg in the triangle, and we can find the shorter leg (n) using the ratio 1:/:2 in a 30°-60°-90° triangle, which would be half of the longer leg. Hence, n = 10 cm / 2 = 5 cm.