Do You Know Your Math? Trigonometry Quiz

Explanation
The Pythagorean Theorem states that in a right-angled triangle, 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. Therefore, the correct formula to find the Pythagorean Theorem is a2 + b2 = c2, where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

Explanation
Pythagoras is the correct answer because he is widely credited with discovering and proving the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem has been fundamental in mathematics and has numerous applications in various fields.

Explanation
The legs of a right triangle are the two sides that form the right angle. In this case, the correct answer is a,b because these two options represent the two sides that form the right angle. Option a,c and b,c are incorrect because they do not represent the sides that form the right angle.

Explanation
The hypotenuse of a right triangle is the side opposite the right angle, and it is always the longest side of the triangle. In this case, option c represents the hypotenuse.

Explanation
The longest side of a right triangle is called the hypotenuse. The hypotenuse is opposite the right angle and is the side that is opposite the right angle. It is also the side that is directly across from the right angle.

Explanation
The given question is asking to find the hypotenuse of a right-angled triangle with the given values of the other two sides, a and b. The formula to find the hypotenuse is c = √(a^2 + b^2). Plugging in the given values of a=12 and b=16 into the formula, we get c = √(12^2 + 16^2) = √(144 + 256) = √400 = 20. Therefore, the correct answer is c=20.

Explanation
The correct answer is c=8.60. This can be calculated using the Pythagorean theorem, which 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 lengths of the other two sides (a and b). In this case, a=5 and b=7. Therefore, c^2 = 5^2 + 7^2 = 25 + 49 = 74. Taking the square root of 74 gives us c=8.60.

Explanation
The given information provides the values of g, c, b, and a. We are asked to find the length of the leg. From the given information, we can see that the value of b is 9.17. Therefore, the length of the leg is 9.17.

Explanation
The length of the leg can be found using 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 lengths of the other two sides. In this case, we are given that c is the hypotenuse and b is one of the legs. Therefore, we can use the formula a = sqrt(c^2 - b^2) to find the length of the other leg. Plugging in the values c=10 and b=7, we get a = sqrt(10^2 - 7^2) = sqrt(100 - 49) = sqrt(51) ≈ 7.14. Therefore, the length of the leg is approximately 7.14.

Explanation
Given that a = 4 and c = 5, we can use the Pythagorean theorem to find the length of the missing side. The 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 lengths of the other two sides (a and b). Therefore, we can use the formula c^2 = a^2 + b^2 to find the missing side. Plugging in the values, we get 5^2 = 4^2 + b^2. Simplifying, we have 25 = 16 + b^2. Subtracting 16 from both sides, we get 9 = b^2. Taking the square root of both sides, we find that b = 3. Therefore, the length of the missing side is 3.