if a right triangle has side length of 37 and 42 what is the third angle
To find the third angle of a right triangle, we need to use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangle are 37 and 42. Using the Pythagorean Theorem:
c^2 = a^2 + b^2
c^2 = 37^2 + 42^2
c^2 = 1369 + 1764
c^2 = 3133
c = √3133
c ≈ 56.02
Now that we know the length of the hypotenuse (c), we can use the sine, cosine, or tangent functions to find the third angle.
Let's calculate the sine of the third angle:
sin(θ) = opposite/hypotenuse
sin(θ) = 37/56.02
sin(θ) ≈ 0.660
To find the third angle, we can use the inverse sine function (sin^-1) on a calculator:
θ = sin^-1(0.660)
θ ≈ 41.72 degrees
Therefore, the third angle of the right triangle is approximately 41.72 degrees.
In the picture, one angle is labeled 22° and lines S and T are parallel. Which other three angles will be 22° ? Separate each angle number with a comma. (1 point)
In the picture where one angle is labeled 22° and lines S and T are parallel, the angles that will also be 22° due to corresponding angles are as follows: 22°, 22°, and 22°.
So, the three angles that will be 22° are: 22°, 22°, 22°.
If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point) Responses Yes, because 3,600 equals 3,600. Yes, because 3,600 equals 3,600. No, because 9,225 does not equal 2,025. No, because 9,225 does not equal 2,025. No, because 5,625 does not equal 3,600. No, because 5,625 does not equal 3,600. Yes, because 5,625 equals 5,625.
To determine if a triangle is a right triangle, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Given the sides of the triangle are 60, 75, and 45, we need to check if the Pythagorean Theorem holds true with these side lengths.
Using the Pythagorean Theorem:
a^2 + b^2 = c^2
Where a and b are the two shorter sides (60 and 45) and c is the hypotenuse (75).
By substituting the side lengths into the equation:
60^2 + 45^2 = 75^2
3600 + 2025 = 5625
Therefore, it is true that 5625 equals 5625, which means that the given triangle is a right triangle.
So, the correct response is:
Yes, because 5,625 equals 5,625.
If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)
To determine if a triangle is a right triangle, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Given the sides of the triangle DEF are 50, 40, and 32, we need to check if the Pythagorean Theorem holds true with these side lengths.
Using the Pythagorean Theorem:
a^2 + b^2 = c^2
Where a and b are the two shorter sides (40 and 32) and c is the hypotenuse (50).
By substituting the side lengths into the equation:
40^2 + 32^2 = 50^2
1600 + 1024 = 2500
Therefore, it is not true that 2500 equals 2624, which means that the given triangle is not a right triangle.
So, the correct answer is: 0
If a triangle has sides of length 12 and 16, how long is the hypotenuse?(1 point)
To find the length of the hypotenuse of a right triangle when the lengths of the two other sides are given, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
Given that the two sides are 12 and 16, we can set up the equation as follows:
a^2 + b^2 = c^2
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
Now, to find the length of the hypotenuse (c), we take the square root of 400:
c = √400
c = 20
Therefore, the length of the hypotenuse of the triangle is 20 units.