MP Board · Class 10 · Mathematics · Introduction to TrigonometryA right-angled triangle has a base of 5 cm and a height of 12 cm. Calculate the length of the hypotenuse using the Pythagorean theorem.
Step-by-Step Solution
Pythagorean Theorem
Formula\nThe Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
\na^2 + b^2 = c^2 \nwhere a and b are the lengths of the other two sides, and c is the length of the hypotenuse.
Given Values\nBase (a) = 5 cm\nHeight (b) = 12 cm
Calculation\nTo find the length of the hypotenuse, we can use the Pythagorean theorem:
\nc^2 = a^2 + b^2\nc^2 = 5^2 + 12^2\nc^2 = 25 + 144\nc^2 = 169
Finding the Length of the Hypotenuse\nTo find the length of the hypotenuse, we take the square root of both sides:
\nc = √169\nc = 13
Conclusion\nTherefore, the length of the hypotenuse is 13 cm.
💡 Study Guide: This question tests core syllabus concepts from Introduction to Trigonometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Trigonometry Revision Notes.