No, it is not a right triangle because \( 7^{2}+5^{2} \neq 8^{2} \) Yes, it is a right triangle because \( 7^{2}+5^{2} \neq 8^{2} \) No, it is not a right triangle because \( 7^{2}+5^{2}=8^{2} \) Yes, it is a right triangle because \( 7^{2}+5^{2}=8^{2} \)

Let’s clarify the situation with our triangle. For a right triangle, the Pythagorean theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. So, if we calculate \( 7^2 + 5^2 \), we find \( 49 + 25 = 74 \), and \( 8^2 = 64 \). Since \( 74 \neq 64 \), it’s clear that this triangle is not a right triangle – it’s missing that special angle! Now, when you're diving into right triangles, it often helps to visualize the relationships with a little help from the world around you. For real-world applications, think about construction or design projects where creating right angles is essential. Builders frequently use the Pythagorean theorem to ensure the structures they create are sturdy and balanced. Whether it’s constructing a roof or laying down a foundation, understanding these relationships can save time and resources while ensuring safety!