Triangle? Yes. Acute, Obtuse, or Right?Right. Explanation: See solution.
Practice makes perfect
First, we want to determine whether the given set of numbers can be the measures of the sides of a triangle. To do that we will use the Triangle Inequality Theorem. We have to check if the sum of each two sides is greater than the third side.
8+15>& 17 âś“
8+17>& 15 âś“
15+17>& 8 âś“
As we can see, the given side lengths can form a triangle. Now, we need to determine if this triangle is acute, right, or obtuse. To do so, we will compare the square of the largest side length to the sum of the squares of the other two side lengths. Let a, b, and c be the lengths of the sides, with c being the longest.
Condition
Type of Triangle
a^2+b^2 < c^2
Obtuse triangle
a^2+b^2 = c^2
Right triangle
a^2+b^2 > c^2
Acute triangle
Let's now consider the given side lengths 8, 15, and 17. Since 17 is the greatest of the numbers, we will let c be 17. We will also arbitrarily let a be 8 and b be 15.
8^2+15^2 ? 17^2
Let's simplify the above statement to determine whether the left-hand side is less than, equal to, or greater than the right-hand side.
