Example Question - hypotenuse length calculation
Here are examples of questions we've helped users solve.
Calculating the Length of the Hypotenuse in a Right Triangle
In this image, we see a right triangle with one side measuring 36 kilometers and another side (which is the opposite of the 90-degree angle) measuring 77 kilometers. The question asks for the length of the hypotenuse, denoted as "c." To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right-angled 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. The formula is: c^2 = a^2 + b^2 Here, a = 36 km and b = 77 km, so we have: c^2 = 36^2 + 77^2 c^2 = 1296 + 5929 c^2 = 7225 Taking the square root of both sides gives us the length of the hypotenuse c: c = √7225 c ≈ 85 Now, rounding to the nearest tenth as requested, we get: c ≈ 85.0 kilometers Therefore, the length of the hypotenuse is approximately 85.0 kilometers.
Calculating the Length of the Hypotenuse of a Right Triangle
The triangle shown in the image is a right triangle, and we are looking for the length of the hypotenuse, denoted as "c". According to the Pythagorean theorem, in a right 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 lengths of the other two sides. This can be written as: c² = a² + b² where c = length of the hypotenuse, a and b = lengths of the other two sides of the right triangle. From the image, we have: a = 60 meters, b = 80 meters. Now we plug these values into the Pythagorean theorem: c² = 60² + 80² c² = 3600 + 6400 c² = 10000 To find c, we take the square root of both sides: c = √10000 c = 100 Therefore, the length of the hypotenuse is 100 meters. Since the problem states that we should round to the nearest tenth if necessary, we can express our final answer as 100.0 meters, although it is not required in this case since 100 is a whole number.
Calculating the Length of the Hypotenuse in a Right-Angled Triangle
The image shows a right-angled triangle with one side measuring 13 cm, which is the height, and the base measuring 23 cm. To solve for the length of the hypotenuse, we can use the Pythagorean theorem, which 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 lengths of the other two sides. Let's denote the hypotenuse as "c". The formula of the Pythagorean theorem is: a² + b² = c² Where: - a = one leg of the triangle (13 cm) - b = the other leg of the triangle (23 cm) - c = the length of the hypotenuse (what we need to find out) So we have: (13 cm)² + (23 cm)² = c² 169 cm² + 529 cm² = c² 698 cm² = c² Now, take the square root of both sides to find the length of the hypotenuse: c = √698 cm² c ≈ √700 cm² c ≈ 26.46 cm Therefore, the length of the hypotenuse is approximately 26.46 cm.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com