In a right triangle, if one angle is 30 degrees, what is the ratio of the length
Practice Questions
Q1
In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees angles? (2019)
1:√3
1:2
√3:1
2:1
Questions & Step-by-Step Solutions
In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees angles? (2019)
Step 1: Understand that a right triangle has one angle that is 90 degrees.
Step 2: Recognize that in a right triangle with one angle of 30 degrees, the other non-right angle must be 60 degrees (because 30 + 60 + 90 = 180).
Step 3: Learn about the special triangle called a 30-60-90 triangle, which has angles of 30 degrees, 60 degrees, and 90 degrees.
Step 4: In a 30-60-90 triangle, the side opposite the 30-degree angle is the shortest side.
Step 5: The side opposite the 30-degree angle is often labeled as '1' (this is a common way to represent it).
Step 6: The side opposite the 60-degree angle is longer and is equal to '√3' times the length of the side opposite the 30-degree angle.
Step 7: Therefore, the ratio of the lengths of the sides opposite the 30-degree angle to the 60-degree angle is 1:√3.
