Assume angle C is a right angle, and given the conditions that c=5 and <B=45 degrees, solve for the side lengths of the right triangle.

Answer 1

Given that angle C is a right angle, the sum of angles A and B in the right triangle is 90 degrees. Since <B = 45 degrees, angle A = 90 - 45 = 45 degrees.

We can use the sine and cosine ratios to find the side lengths of the right triangle.

For angle A, we can use the sine ratio:
sin A = opposite/hypotenuse
sin 45 = a/5
√2/2 = a/5
a = 5 * √2/2
a = 5√2/2

For angle A, we can use the cosine ratio:
cos A = adjacent/hypotenuse
cos 45 = b/5
√2/2 = b/5
b = 5 * √2/2
b = 5√2/2

Therefore, the side lengths of the right triangle are:
a = 5√2/2
b = 5√2/2
c = 5