Final answer:
In a right triangle with angle bisector, we can use the Pythagorean theorem to find the length of the hypotenuse and the given measures of the angles.
Step-by-step explanation:
In a right triangle ABC, where angle C is 90 degrees and line BL is the angle bisector of angle ABC, we can use the properties of right triangles and angle bisectors to find various measures.
First, we know that in a right triangle, the two shorter sides are called legs, and the longest side is called the hypotenuse. By the Pythagorean theorem, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse (a^2 + b^2 = c^2). So, if we know the measures of the legs, we can calculate the length of the hypotenuse.
Second, as line BL is the angle bisector of angle ABC, it divides the angle into two equal parts. So, we can use this information to find the measures of the angles in the triangle.