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Find Unknown Leg x in Right-Angled Triangle with Hypotenuse 14 mm and Leg 0.5 cm
Mathematics
Grade 8 (Junior High School)
Question Content
Find the length of the unknown side x in the right-angled triangle (i) with one leg 0.5 cm, hypotenuse 14 mm. (Note: Convert units to be consistent first.)
Correct Answer
≈13.08 mm or √171.75 mm
Detailed Solution Steps
1
Step 1: Convert all side lengths to the same unit. Convert 0.5 cm to mm: 0.5 cm = 5 mm.
2
Step 2: Apply the Pythagorean theorem (a² + b² = c²) where c = 14 mm (hypotenuse), b = 5 mm (known leg), and x is the unknown leg a.
3
Step 3: Rearrange the formula to solve for x: x² = c² - b².
4
Step 4: Substitute the values: x² = (14)² - (5)² = 196 - 25 = 171.75.
5
Step 5: Take the square root to find x: x = √171.75 ≈13.08 mm.
Knowledge Points Involved
1
Pythagorean Theorem with Mixed Units
When solving right-angled triangle problems with mixed units, all measurements must be converted to the same unit before applying the Pythagorean theorem to avoid incorrect calculations. This is critical for ensuring the accuracy of side length calculations.
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