What's the missing side length in simplest form of 45 degrees, 45, & 10
To find the missing side length, we can use the trigonometric functions sine, cosine, or tangent.
In this case, since we know the angle (45 degrees) and the adjacent side length (10), we can use the cosine function. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
Using the cosine function:
cos(45) = adjacent / hypotenuse
cos(45) = 10 / hypotenuse
To solve for the hypotenuse, we isolate the variable:
hypotenuse = 10 / cos(45)
To simplify the expression, we can use the fact that cos(45) is equal to √2/2:
hypotenuse = 10 / (√2/2)
Now, let's rationalize the denominator by multiplying the numerator and denominator by √2:
hypotenuse = (10 * √2) / (√2/2)
hypotenuse = (10 * √2) * (2/√2)
Simplifying, we get:
hypotenuse = (20 * √2) / 2
hypotenuse = 10√2
Therefore, the missing side length, in simplest form, is 10√2.
To determine the missing side length of a right triangle with a 45° angle, side length of 45, and another given side length of 10, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the missing side length "x".
In this case, we have:
45° angle -> both legs are congruent
Side length = 45
Another side length = 10
Using the Pythagorean theorem:
x^2 + 45^2 = 10^2
Simplifying:
x^2 + 2025 = 100
Subtracting 2025 from both sides:
x^2 = -1925
Since the result is a negative number, it means that there is no real solution for the missing side length of this triangle.
Thus, the missing side length cannot be determined for the given information.