Pythagoras’ theorem is one of the most fundamental mathematical theories of all time, and trigonometry is a branch of mathematics that uses the theorem to solve right-angled triangle problems. Homework 1 for Unit 12 Trigonometry covers the theorem in great detail and requires students to answer questions about it. To help students understand the answers, this article provides a detailed explanation of the theorem and the different types of calculations that are required to solve a problem.

## Understanding the Pythagorean Theorem and Its Uses

The Pythagorean theorem states that in any right-angled triangle, the sum of the squares of the two shorter sides (a and b) will equal the square of the longest side (c). This can be written as a2 + b2 = c2. The theorem can be used to solve right-angled triangle problems by using the values of two sides to calculate the value of the third side. The theorem is also used to calculate the area of a right-angled triangle.

## Using the Theorem to Solve Trigonometry Problems

The Pythagorean theorem is used to solve trigonometry problems by determining the length of one side of a right-angled triangle when the lengths of the other two sides are known. For example, if the lengths of two sides of a triangle are 4 and 5, then the length of the third side can be determined by using the theorem. Using the equation a2 + b2 = c2, the length of the third side (c) can be calculated as c = √(4² + 5²) = 6.403.

## Applying the Theorem to Determine Area

The theorem can also be used to calculate the area of a right-angled triangle. To do this, the lengths of the two shorter sides (a and b) must be known. The area of the triangle can then be calculated using the formula A = ½ab. For example, if the length of the two shorter sides of a triangle are 4 and 5, then the area of the triangle can be calculated as A = ½ x 4 x 5 = 10.

The Pythagorean theorem is an important mathematical theory that is used to solve right-angled triangle problems. It states that the sum of the squares of the two shorter sides of a right-angled triangle will equal the square of the longest side. The theorem is used to determine the length of the third side when the lengths of two other sides are known. It can also be used to calculate the area of a right-angled triangle. Unit 12 Trigonometry Homework 1 covers the theorem in great detail and requires students to answer questions about it.