A triangle has sides that measure 16 inches, 15 inches, and 22 inches. Will it be acute, obtuse, or right?
gotta show how I got my answer
Thanks guys!
Your previous 5 questions are all basically the same.
I will do this one, you do the others.
Let's assume that we have a right-angled triangle, then 22 must be the hypotenuse, and
16^ + 15^2 = 22^2
but 16^ + 15^2 = 481
and 22^2 =484 , so we DON'T have a right angle.
But c^2 > a^2 + b^2
so the angle opposite of c must be larger than 90°, which makes the
triangle an obtuse triangle
( if c^2 < a^2 + b^2 , then the angle opposite of c must be smaller than 90°, which makes the triangle an acute triangle)
I need help please
To determine whether a triangle is acute, obtuse, or right, we need to examine the relationships between the lengths of its sides.
1. Acute Triangle: All three angles of an acute triangle are less than 90 degrees.
2. Obtuse Triangle: One angle of an obtuse triangle is greater than 90 degrees.
3. Right Triangle: One angle of a right triangle is exactly 90 degrees.
To find out which category the given triangle falls into, let's follow these steps:
Step 1: Identify the longest side.
The longest side in the given triangle measures 22 inches.
Step 2: Compare the sum of the squares of the two shorter sides to the square of the longest side using the Pythagorean theorem.
According to the Pythagorean theorem, in a right triangle, the square of the longest side is equal to the sum of the squares of the other two sides.
16^2 + 15^2 = 256 + 225 = 481
22^2 = 484
Step 3: Analyze the results.
If the sum of the squares of the two shorter sides is equal to the square of the longest side (481 = 484), the triangle will be "right."
Therefore, the triangle with sides measuring 16 inches, 15 inches, and 22 inches is a right triangle.
By using the Pythagorean theorem, we determined that the given triangle is a right triangle because the sum of the squares of the two shorter sides (16^2 + 15^2 = 481) is equal to the square of the longest side (22^2 = 484).