Example Question - right triangle theorem
Here are examples of questions we've helped users solve.
Calculating the Length of the Third Leg in a Right Triangle
The image shows a right triangle with one leg of length 7, the hypotenuse of length 9, and the other leg (which we want to find) labeled 'x'. To solve for 'x', we can use the Pythagorean theorem, which states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the following equation holds true: a² + b² = c² Here, 'a' is 7, 'b' is 'x', and 'c' is 9. Plugging in the values we have: 7² + x² = 9² 49 + x² = 81 Now we'll solve for x²: x² = 81 - 49 x² = 32 Taking the square root of both sides to solve for 'x': x = √32 Now we can calculate the value of 'x' and round it to the nearest tenth: x ≈ 5.7 So, 'x' rounded to the nearest tenth is approximately 5.7.
Determining Angle Measures in Triangles
To find the measure of the indicated angle in the triangle, we can use the Pythagorean theorem if the triangle is a right triangle. The Pythagorean theorem states that for a right triangle with legs a, b and hypotenuse c, the relationship between the sides is given by: a^2 + b^2 = c^2 Based on the numbers provided (42 and 40), it looks like they could represent the lengths of the legs of a right triangle with the hypotenuse unknown. But since there's no indication the angle we're solving for is the right angle (90 degrees) and we don't have additional information confirming that the triangle is a right angle, we cannot assume it's a right triangle just based on this image. However, assuming this is a right triangle, with 42 and 40 as the lengths of the two legs, we can determine the measure of the indicated angle (which, in this case, would be the right angle). A right angle is always 90 degrees, so if this assumption holds, the answer would be 90 degrees. Without a clear indication of a right angle or additional information, we cannot conclusively determine the measure of the indicated angle using the numbers given. If you have more information about the triangle (such as it being a right angle or not), please provide it so I can help you further. Otherwise, based on the image alone, the question cannot be solved.
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