Final answer:
To find the length of the horizontal side of a right triangle with an angle of π/4 rad and a hypotenuse of 6 inches, apply the Pythagorean theorem to an isosceles right triangle. The calculation yields a horizontal side length of approximately 4.2 inches when rounded to the nearest tenth.
Step-by-step explanation:
If a right triangle has an angle of π/4 rad and a hypotenuse of 6 inches, we can use trigonometric functions to find the length of the horizontal side. Since the angle is π/4 rad (45 degrees), we know that this is an isosceles right triangle where the adjacent side (horizontal side) is equal in length to the opposite side (vertical side). Using the Pythagorean theorem a² + b² = c² where a and b are the lengths of the legs and c is the length of the hypotenuse, we can calculate the length as follows:
- Let a be the length of the horizontal side, then a = b because of the isosceles right triangle property.
- Apply the theorem: a² + a² = 6² (since the hypotenuse is 6 inches).
- Simplify to get 2a² = 36.
- Solve for a: a² = 18.
- Take the square root of both sides: a = √18.
- Rounded to the nearest tenth: a ≈ 4.2 inches.
Therefore, the length of the horizontal side is approximately 4.2 inches.