Question

A conjecture and the flowchart proof used to prove the conjecture are shown. Given: m ∠QRS=76°, Prove: △PQR is an obtuse triangle. Drag and drop a statement to each box to complete the proof.

a) True
b) False

Answer 1

The true/false question addresses whether the Pythagorean theorem is applicable for calculating the length of a resultant vector from two perpendicular vectors. The answer is True, as the theorem accurately calculates the hypotenuse in a right-angled triangle formed by the vectors.

Step-by-step explanation:

The question posed pertains to the use of the Pythagorean theorem to calculate the length of a resultant vector that is derived from the addition of two vectors at right angles to one another. The Pythagorean theorem can indeed be used in such a scenario, making the correct answer to the question True.

The theorem is a fundamental principle in mathematics that states that in a right-angled triangle, 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. This theorem can be expressed as a² + b² = c². When applied to vectors, if two vectors are perpendicular, they can form the adjacent sides of a right-angled triangle, and their resultant vector will be the hypotenuse, with its length calculable by the theorem.