Question

question 2
which triangle is a right triangle based on side lengths?
6, 12, 13
7, 8, 10
4, 5, 6
9, 10, 18
question 3
which situation would require using the pythagorean theorem?
finding the diagonal of a rectangular tv screen
finding a missing angle
calculating the area of a square

Explanation:

Step1: Check each option for question 2 using Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the longest side).

• For \(6,12,13\): \(6^{2}+12^{2}=36 + 144=180\), \(13^{2}=169\), \(180

eq169\)

• For \(7,8,10\): \(7^{2}+8^{2}=49+64 = 113\), \(10^{2}=100\), \(113

eq100\)

• For \(4,5,6\): \(4^{2}+5^{2}=16 + 25=41\), \(6^{2}=36\), \(41

eq36\)

• For \(9,10,18\): \(9^{2}+10^{2}=81+100 = 181\), \(18^{2}=324\), \(181

eq324\)

Wait, there is a mistake. Let's re - check:

• For \(7,8,10\): \(7^{2}+8^{2}=49 + 64=113

eq100\)

• For \(6,12,13\): \(6^{2}+12^{2}=36+144 = 180

eq169\)

• For \(4,5,6\): \(4^{2}+5^{2}=16 + 25=41

eq36\)

• For \(a = 7,b = 8,c = 10\) (wrong). Let's check \(6,12,13\) again.

Wait, no. Let's check \(7,8,10\) again.
Wait, no. Let's check \(a = 6,b = 12,c = 13\): \(a^{2}+b^{2}=6^{2}+12^{2}=36 + 144=180\), \(c^{2}=13^{2}=169\)
Wait, no. Let's check \(a = 7,b = 8,c = 10\): \(a^{2}+b^{2}=7^{2}+8^{2}=49+64 = 113\), \(c^{2}=10^{2}=100\)
Wait, no. Let's check \(a = 4,b = 5,c = 6\): \(a^{2}+b^{2}=4^{2}+5^{2}=16 + 25=41\), \(c^{2}=6^{2}=36\)
Wait, no. Let's check \(a = 9,b = 10,c = 18\): \(a^{2}+b^{2}=9^{2}+10^{2}=81+100 = 181\), \(c^{2}=18^{2}=324\)

Wait, there is a mistake in the problem. Maybe it's a typo. But if we assume the first question is wrong (maybe the intended answer is not in the options, but if we consider Pythagorean theorem application for question 3:

Step2: Analyze question 3

• The Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) is used to find the length of a side (usually the hypotenuse) in a right - triangle. A rectangular TV screen's diagonal forms a right - triangle with the length and width of the screen. So, finding the diagonal of a rectangular TV screen requires the Pythagorean theorem.
• Finding a missing angle usually requires trigonometric ratios (\(\sin\theta=\frac{a}{c},\cos\theta=\frac{b}{c},\tan\theta=\frac{a}{b}\)).
• Calculating the area of a square uses \(A = s^{2}\) (where \(s\) is the side length)

Answer:

For question 2: None of the options \(6,12,13\); \(7,8,10\); \(4,5,6\); \(9,10,18\) form a right - triangle. For question 3: Finding the diagonal of a rectangular TV screen.