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Find Unknown Leg x in Right-Angled Triangle with Hypotenuse 26 cm and Leg 17 cm
Mathematics
Grade 8 (Junior High School)
Question Content
Find the length of the unknown side x in the right-angled triangle (h) with one leg x, hypotenuse 26 cm, and the other leg 17 cm.
Correct Answer
≈20.02 cm or √407 cm
Detailed Solution Steps
1
Step 1: Apply the Pythagorean theorem (a² + b² = c²) where c is the hypotenuse, a = x (unknown leg), b = 17 cm, c = 26 cm.
2
Step 2: Rearrange the formula to solve for the unknown leg: a² = c² - b², so x² = 26² - 17².
3
Step 3: Calculate the squares: 676 - 289 = x², so x² = 407.
4
Step 4: Take the square root to find x: x = √407 ≈ 20.02 cm.
Knowledge Points Involved
1
Pythagorean Theorem (Rearranged for Legs)
A variation of the Pythagorean theorem used to find the length of a missing leg in a right-angled triangle. The formula is rearranged to leg² = hypotenuse² - known leg², which is used when the hypotenuse and one leg are known, and the second leg is unknown.
2
Exact vs. Approximate Radical Values
Exact values are expressed in radical form (e.g., √407) when the number under the square root is not a perfect square, while approximate values are decimal estimates calculated using a calculator. Exact form is used for precision, while approximate form is used for practical, real-world measurements.
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