The triangle has side lengths of 25 in, 26in, and 3.5 in. classify acute, obtuse, or right

Obtuse triangle

Step-by-step explanation:

The longest side of the triangle is 26 in, so that will be the hypotenuse.

By an extension of the Pythagorean theorem:

Where a and b are the legs, and c is the hypotenuse.

Plug in: 3.5² + 25² ₙ 26²

Powers: 12.25 + 625 ₙ 676

Add: 637.25 < 676.

That means that this triangle is obtuse.

Obtuse

Step-by-step explanation:

Using law of cosine, we can find the angle between the shorter sides:

c² = a² + b² − 2ab cos C

26² = 25² + 3.5² − 2(25)(3.5) cos C

cos C ≈ -0.221

C ≈ 102.8°

102.8° is greater than 90°, so the triangle is obtuse.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

a. the residual plot for model 1 has a random pattern and is a good fit for the data.