Math Is Fun Forum

Let's consider a right-angled triangle with one side of length 3 units and another side of length 4 units. We want to calculate one of the angles using basic geometry and the Pythagorean theorem.
Apply the Pythagorean theorem: According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:

Hypotenuse² = 3² + 4²
Hypotenuse² = 9 + 16
Hypotenuse² = 25

Taking the square root of both sides, we get:
Hypotenuse = √25
Hypotenuse = 5 units

Determine the angle: Now, we can calculate one of the angles using basic geometry. Since we know the lengths of two sides, we can use the concept of ratios of sides in similar triangles.

In this case, we can consider another right-angled triangle with sides in the ratio of 3:4:5. This triangle is similar to the original triangle, but with all side lengths multiplied by a common factor.

The smaller triangle (3:4:5) is a well-known Pythagorean triple, so we know the angle opposite the side of length 3 is 37 degrees (approximately). Thus, the angle in the original triangle is also approximately 37 degrees.
So, in this example, the angle in the triangle is approximately 37 degrees.