In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
Practice Questions
1 question
Q1
In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
5 cm
10 cm
8 cm
7 cm
Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
Solution: Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.
Steps: 7
Step 1: Identify the right triangle and the given information: one angle is 30 degrees and the hypotenuse is 10 cm.
Step 2: Recall the relationship between the angles and sides in a right triangle. The side opposite the 30-degree angle can be found using the sine function.
Step 3: Use the sine function: sin(30°) = opposite side / hypotenuse.
Step 4: Substitute the known values into the equation: sin(30°) = opposite side / 10 cm.
Step 5: Since sin(30°) equals 1/2, rewrite the equation: 1/2 = opposite side / 10 cm.
Step 6: To find the opposite side, multiply both sides by 10 cm: opposite side = 10 cm * 1/2.
Step 7: Calculate the result: opposite side = 5 cm.
