Find the unknown sides and acute angles of a right-angled triangle if its hypotenuse and leg are, respectively, 14m 6m.

The second leg of this triangle can be found by the Pythagorean theorem. According to her, it is equal to the square root of the difference between the hypotenuse and the first leg. Let’s find it:

√ (14² – 6²) = √ (196 – 36) = √160 = 4√10 ≈ 12.6 m.

The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse. Find the sine of the first angle, let it be angle A:

sin A = 6/14 = 3/7.

From here

angle A ≈ 25º.

The sum of the angles in any triangle is 180º. So the second angle, let’s designate it as angle B, will be equal to:

angle B ≈ 180º – 90º – 25º ≈ 90º – 25º ≈ 65º.

Answer: the second leg of a right-angled triangle is approximately 12.6 m, and its unknown angles are approximately equal to 25º and 65º.