Find the value of x in the following triangles.
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, the lengths of the two non-hypotenuse sides are known. Plug in a = 3 and b = 5 and solve for x that represents the lengh of the hypotenuse:
3^2 + 5^2 = x^2
9 + 25 = x^2
36 = x^2
Since the length of the hypothenuse is positive we get:
x = \sqrt{34}
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, the lengths of the two non-hypotenuse sides are known. Plug in a = 6 and b = 8 and solve for x that represents the lengh of the hypotenuse:
6^2 + 8^2 = x^2
36 + 63 = x^2
100 = x^2
Since the length of the hypothenuse is positive we get:
x= 10
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, we know the lengths of the hypothenuse and the length of another side. Plug in a = 3 and c = 5 and solve for x :
3^2 + x^2 = 5^2
9 + x^2= 25
x^2=16
Since x is a positive number, we get:
x= 4
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, we know the length of the hypothenuse and the length of another side. Plug in b = 5 and c = 8 and solve for x :
x^2 + 5^2 = 8^2
x^2+ 25 = 64
x^2=39
x = \sqrt{39}
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, we know the length of the hypothenuse and the length of another side. Plug in b = 5 and c = 10 and solve for x :
x^2 + 5^2 = 10^2
x^2+ 25 = 100
x^2=75
Since x is a positive number, we get:
x = \sqrt{75}
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, the lengths of the two non-hypotenuse sides are known. Plug in a = 5 and b = 5 and solve for x that represents the length of the hypotenuse:
5^2 + 5^2 = x^2
25 + 25 = x^2
50 = x^2
Since the length of the hypothenuse is positive we get:
x=\sqrt{50}
The Pythagorean Theorem relates the side lengths of a right triangle:
a^2 + b^2 = c^2
Where c is the length of the hypotenuse and a and b are the lengths of the other two sides. If two side lengths are known, the third can be calculated using this theorem.
In this problem, the lengths of the two non-hypotenuse sides are known. Plug in a=\sqrt{3} and b = 5 and solve for x that represents the length of the hypotenuse:
\left(\sqrt{3}\right)^2 + 5^2 = x^2
3 + 25 = x^2
28 = x^2
Since the length of the hypothenuse is positive we get:
x=\sqrt{28}