Question

Find the lengths of the remaining sides of the triangle.

[c = 18√2, a = 45⁰] angle
a) (b = 18)
b) (b = 18√3)
c) (b = 36)
d) (b = 36√2)

Answer 1

To find the length of side b in a right triangle given the lengths of the other two sides, we can use the Pythagorean theorem. However, in this case, side b does not have a real length.

Step-by-step explanation:

To find the length of side b in a right triangle given the lengths of the other two sides, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). So in this case, we have c = 18√2 and a = 45°. To find b, we can rearrange the equation and solve for b: b² = c² - a². Plugging in the values, we get b = √((18√2)² - (45°)²).

Expanding the equation, we have b = √(648 - 2025).

Simplifying further, we have b = √(-1377).

Since the square root of a negative number is not a real number, it means that side b does not have a real length in this case. Therefore, none of the given options (b = 18, b = 18√3, b = 36, b = 36√2) are correct.