Right triangles and Trig. Unit test part 1
A triangle has side lengths of 34 in., 20 in., and 47 in. Is the triangle acute, obtuse, or right?
do u have brainly?
Not brainly plus I done run out of questions on there LOL
wdym? you cant run out of questions on brainly. all you have to do is answer someone else's question to get points, which you then use to ask your own questions
To determine whether the triangle is acute, obtuse, or right, we need to check the relationship between the side lengths.
In a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. This is known as the Pythagorean theorem.
Let's apply the Pythagorean theorem to the given triangle:
Side lengths: 34 in., 20 in., and 47 in.
To find the longest side (hypotenuse), we can compare the squares of the side lengths:
34^2 = 1156
20^2 = 400
47^2 = 2209
Based on the Pythagorean theorem, the sum of the squares of the two shorter sides must be equal to the square of the longest side.
In this case, 1156 + 400 = 1556, which is not equal to 2209. Therefore, the triangle is not a right triangle.
To determine whether it is acute or obtuse, we can use the Law of Cosines, which states that in a triangle, the square of one side equals the sum of the squares of the other two sides, minus twice their product, multiplied by the cosine of the included angle.
Let's calculate the cosine of the largest angle using the Law of Cosines:
Cosine of largest angle = (20^2 + 34^2 - 47^2) / (2 * 20 * 34)
Simplifying the equation, we have:
Cosine of largest angle = (-1200) / (1360)
Cosine of largest angle ≈ -0.88
Now, to determine whether the triangle is acute or obtuse, we need to find the largest angle (the angle opposite the longest side) and determine its cosine value.
Since the cosine of an acute angle is positive and the cosine of an obtuse angle is negative, we can conclude that the triangle is acute.
Therefore, the triangle with side lengths 34 in., 20 in., and 47 in. is an acute triangle.
Note: Calculators or online tools can assist with performing the necessary calculations if you have access to them.