Understanding the Problem
You have a right triangle where two sides are given: 7 cm and 2 cm. You want to find the length of side B.
Step 1: Identify the sides
The Pythagorean theorem states:
a² + b² = c²
where c is the hypotenuse (the longest side opposite the right angle), and a and b are the other two sides.
First, determine which side is the hypotenuse. Between 7 cm and 2 cm, 7 cm is larger, so likely 7 cm is the hypotenuse or one of the legs. However, the problem doesn't specify which sides these lengths correspond to or which side B is.
Step 2: Clarify what is side B
There are two possible cases:
- Case 1: Side B is one of the legs, and the hypotenuse is 7 cm. Then one leg is 2 cm, side B is unknown.
- Case 2: Side B is the hypotenuse, and the legs are 7 cm and 2 cm.
Step 3: Solve for side B in each case
Case 1: Hypotenuse = 7 cm, one leg = 2 cm, find B (other leg)
Using the Pythagorean theorem:
b² + 2² = 7²
b² + 4 = 49
Subtract 4 from both sides:
b² = 49 - 4 = 45
Take the square root:
b = √45 = √(9 × 5) = 3√5 ≈ 6.71 cm
Case 2: Legs = 7 cm and 2 cm, find B (hypotenuse)
b² = 7² + 2²
b² = 49 + 4 = 53
Take the square root:
b = √53 ≈ 7.28 cm
Conclusion
So depending on what side B is (a leg or the hypotenuse), the answer is:
- If B is a leg and hypotenuse is 7 cm: B ≈ 6.71 cm
- If B is the hypotenuse and legs are 7 cm and 2 cm: B ≈ 7.28 cm
Please confirm which side B represents to use the appropriate solution.