Final answer:
To find x and y, use the Pythagorean Theorem, which in a right triangle connects the lengths of the legs a and b with the hypotenuse c through the formula a² + b² = c². Calculate the hypotenuse by taking the square root of the sum of the squares of the other two sides, and find angles using trigonometric functions.
Step-by-step explanation:
Finding x and y Using Pythagorean Theorem
To find the values of x and y, you will need to apply the Pythagorean Theorem, which states that in a right-angled 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). This can be expressed as:
a² + b² = c²
By rearranging the formula, we can solve for one of the legs if we know the hypotenuse and the other leg, or calculate the hypotenuse if we know both legs:
c = √(a² + b²)
or
b = √(c² - a²)
For instance, if you are given a = 9 blocks and b = 5 blocks, the hypotenuse c can be calculated as:
c = √(9² + 5²)
This would give you the length of the hypotenuse. To find the angle of the triangle, you can use trigonometric ratios such as the tangent:
θ = tan⁻¹(b/a)
This will give you the direction in degrees. When you have the values of x and y, round the final answers to the nearest tenth.
Example Calculation
If x and y are legs of a right triangle, with x = 9 and y = 5, and we are looking to find the hypotenuse (let's call it z), the Pythagorean Theorem would be:
z = √(x² + y²)
Plugging in the values:
z = √(9² + 5²) = √(81 + 25) = √106
After calculating the square root, we would round z to the nearest tenth.