Final answer:
In a right triangle, the sum of the interior angles is always 180 degrees, with one angle being 90 degrees. The Pythagorean theorem is used to calculate the length of the hypotenuse when the lengths of the other two sides are known. The direction can be calculated using the tangent function.
Step-by-step explanation:
When considering triangle ABC as a right triangle, with angle A measuring 90 degrees, we're dealing with the basic properties of a triangle and the Pythagorean theorem. Every triangle has three sides that lie on a plane, with the sum of the interior angles adding up to 180 degrees. Specifically, in a right triangle, where one angle measures 90 degrees, the Pythagorean theorem applies and states that 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.
For example, if in triangle ABC, side Ax and side Ay are known, then the length of the hypotenuse A can be calculated using the formula A = √(Ax² + Ay²). Furthermore, if the lengths of Ax and Ay are 9 and 5 blocks respectively, then the hypotenuse A would be √(9² + 5²), which equals approximately 10.3 blocks. If we need to find the direction, we can use the tangent function, tan⁻¹(Ay/Ax), which would be tan⁻¹(5/9) in this case, resulting in an angle of approximately 29.1 degrees.