Example Question - leg length
Here are examples of questions we've helped users solve.
Solving for Missing Leg Length in Right Triangle
The image shows a right triangle with one leg labeled as 75 cm and the hypotenuse labeled as 72 cm. We are asked to solve for the length of the missing leg, which I'll refer to as 'b'. There's an error in the labeling because the hypotenuse is the longest side of a right triangle and cannot be shorter than any other side. In a right triangle, the hypotenuse should always be the longest side, and both legs should be shorter than the hypotenuse. But we can proceed as if the values provided were for a leg and the hypotenuse, just reversing them in our application of the Pythagorean theorem. Assuming the provided measurements were mistakenly switched, with 72 cm being a leg instead of the hypotenuse, we can use the Pythagorean theorem to solve for 'b'. The Pythagorean theorem states that in a right-angled triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c), or a^2 + b^2 = c^2. Let's plug in the provided values (with 75 cm as the hypotenuse in our calculations due to the error): a^2 + b^2 = c^2 72^2 + b^2 = 75^2 5184 + b^2 = 5625 Subtract 5184 from both sides to solve for b^2: b^2 = 5625 - 5184 b^2 = 441 Now, take the square root of both sides to find the value of 'b': b = √441 b = 21 So the missing leg 'b' of the right triangle is 21 centimeters, provided the values given were mixed up and we interpret the labeled 72 cm side as a leg and not the hypotenuse.
Solving for Missing Leg Length in a Right-Angled Triangle
This image shows a right-angled triangle with one leg of length 75 cm, the hypotenuse of length 72 cm, and the length of the other leg labeled "b." In a right-angled triangle, the Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as: c² = a² + b² where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. However, from the diagram, we see that they've incorrectly labeled the hypotenuse as shorter than one of the legs, which cannot be the case. So, let's assume that 72 cm is actually the other leg, and "c" represents the hypotenuse of 75 cm. Then we have: c² = a² + b² Solving for b, the equation becomes: b² = c² - a² Substitute the given values: b² = 75² - 72² b² = 5625 - 5184 b² = 441 Next, find the square root of both sides to solve for b: b = √441 b = 21 Therefore, the length of the missing leg b is 21 centimeters.
Calculation of Leg Length in 45-45-90 Triangle
This image depicts a right triangle, where one of the angles is 45 degrees and the hypotenuse opposite this angle measures 5 units. Since this is a 45-45-90 triangle, the two legs are congruent. In a 45-45-90 right triangle, the legs are each \( \frac{1}{\sqrt{2}} \) (which is the same as \( \sqrt{2}/2 \)) times the length of the hypotenuse. Let's call the length of each leg \( x \). Then: \[ x = \frac{1}{\sqrt{2}} \times 5 = \frac{5}{\sqrt{2}} \] However, it's often preferred to rationalize the denominator, so we multiply the numerator and denominator by \( \sqrt{2} \): \[ x = \frac{5\sqrt{2}}{\sqrt{2}\times\sqrt{2}} = \frac{5\sqrt{2}}{2} \] Therefore, the length of each leg of the triangle is \( \frac{5\sqrt{2}}{2} \) units.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com