Example Question - triangle hypotenuse
Here are examples of questions we've helped users solve.
Calculating Distance in Right-Angled Triangle
The problem seems to describe a right-angled triangle, with the slide forming one leg west of the tire swing and another leg south of the monkey bars. The distance between the slide and the tire swing is 2 meters, which is one leg of the triangle. The distance between the tire swing and the monkey bars is 3 meters, which is the other leg of the triangle. We need to find the hypotenuse of the triangle, which will be the distance from the slide to the monkey bars. This can be solved using the Pythagorean theorem. The theorem states that for a right-angled triangle with legs a and b, and hypotenuse c, c² = a² + b² Let's substitute the given values: c² = 2² + 3² c² = 4 + 9 c² = 13 Now, we take the square root of both sides to solve for c: c = √13 The exact distance is the square root of 13. However, if you want the answer rounded to the nearest tenth, you will need to calculate the square root. √13 ≈ 3.6 So, the slide is approximately 3.6 meters away from the monkey bars.
Calculating the Length of GH in a Right Triangle
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 - HD Since GD = 13 and HD = 9 (from the information given in the image), GH = 13 - 9 = 4 units Now we have the lengths of both legs of triangle FED: GD = 13 units ED = 3 units We can now find the hypotenuse FE using the Pythagorean theorem: FE^2 = GD^2 + ED^2 FE^2 = 13^2 + 3^2 FE^2 = 169 + 9 FE^2 = 178 FE = √178 Since 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 / 2 GH = √178 / 2 This 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.
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