In a triangle ABC, angle = 90 degrees, angle A = 45 degrees AC = 2√2. Find AB.

Given:

ABC – right triangle;

Angle C = 90 degrees;

Angle A = 45 degrees;

AC = 2√2;

Find AB.

Solution:

1) Since angle C is 90 degrees and angle A is 45 degrees, then angle B is:

180 – 90 – 45 = 45 degrees.
Hence, angle B = angle A = 45 radices.

2) In order to find the hypotenuse AB of the triangle ABC, we use the formula:

cos A = AC / AB.

Hence, AB = AC / cos a;

Substitute the known values into the formula and find the hypotenuse AB.

AB = 2√2 / cos 45 = 2√2 / (√2 / 2) = 2√2 * 2 / √2 = 2 * 2 = 4;

Answer: AB = 4.