Final answer:
To find the length of the horizontal side of a right triangle with an angle of pi/4 rad and a hypotenuse of 6 inches, we determine that the triangle is isosceles and apply the Pythagorean theorem. The calculation gives us a horizontal side length of 4.24 inches.
Step-by-step explanation:
Finding the Length of the Horizontal Side of a Right Triangle
If a right triangle has an angle of pi/4 rad and a hypotenuse of 6 inches, to find the length of the horizontal side, we can use trigonometric ratios. Since the triangle is a right triangle with an angle of pi/4, it means that the triangle is an isosceles right triangle where the two legs are equal in length.
Using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), i.e., a² + b² = c², we can calculate the length of the horizontal side.
Let 'x' be the length of both the horizontal and the vertical sides since the given right triangle is isosceles. Hence, x² + x² = 6², which simplifies to 2x² = 36. When we solve for 'x,' we get x = √(36/2) which equals √18. After finding the square root, the length of the horizontal side is 4.24 inches (using two decimal places).
In this scenario, we have used trigonometric concepts associated with right triangles and applied the Pythagorean theorem to find the length of the horizontal side.