Question - Calculating the Length of GH in a Right Triangle
Solution:
To solve for GH, we will use the properties of right triangles and the Pythagorean theorem. From the image, it looks like we have a right triangle with GE as the hypotenuse, and segments GH and ED as the other two sides.We are given:- ED = 3 units (vertical leg)- GD = 13 units (horizontal leg)Using the Pythagorean theorem (a^2 + b^2 = c^2) for right triangle FED, where a and b are the legs and c is the hypotenuse (FE in this case), we can calculate the length of FE.First, we find the length of GD by subtracting the length of HD from GH:GH = GD - HDSince GD = 13 and HD = 9 (from the information given in the image),GH = 13 - 9 = 4 unitsNow we have the lengths of both legs of triangle FED:GD = 13 unitsED = 3 unitsWe can now find the hypotenuse FE using the Pythagorean theorem:FE^2 = GD^2 + ED^2FE^2 = 13^2 + 3^2FE^2 = 169 + 9FE^2 = 178FE = √178Since GE is the diameter of the circle, which is FE here, and G to H is the radius, GH is half of GE:GH = FE / 2GH = √178 / 2This is the length of GH in terms of the square root. If a decimal value is needed, we would calculate the square root of 178 and then divide by 2 to find GH. However, the value appears to be a radical rather than a decimal, so GH = √178 / 2.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com