Question - Calculating Hypotenuse Using Pythagorean Theorem
Solution:
The Pythagorean Theorem states that for a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as:\[ c^2 = a^2 + b^2 \]In the given triangle, the lengths of the two sides (a and b) are 4 and 8, respectively. Let's use this information to find the length of the hypotenuse (c):\[ c^2 = 4^2 + 8^2 \]\[ c^2 = 16 + 64 \]\[ c^2 = 80 \]Now we'll find the square root of both sides to solve for c:\[ c = \sqrt{80} \]The exact value of √80 can be simplified by factoring out squares from 80:\[ \sqrt{80} = \sqrt{16 \cdot 5} \]\[ \sqrt{80} = \sqrt{16} \cdot \sqrt{5} \]\[ \sqrt{80} = 4\sqrt{5} \]Therefore, the exact value of c is:\[ c = 4\sqrt{5} \]
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com