# In a right-angled triangle, one of the acute angles is 60 °, and the leg adjacent to it is 12 cm.

September 12, 2021 | education

| **In a right-angled triangle, one of the acute angles is 60 °, and the leg adjacent to it is 12 cm.Find the lengths of the segments by which the height drawn from the vertices of the right angle divides the hypotenuse**

1. A, B, C – the vertices of the triangle. ∠С = 90 °. ∠А = 60 °. CE – height. AC = 12 cm.

2. We calculate the length of the segment AE through the cosine ∠A:

AE / AC = cosine ∠A = cosine 60 ° = 1/2.

AE = AC x 1/2 = 12 x 1/2 = 6 cm.

3. We calculate the length of the leg of the BC rectangular ΔABS through the tangent ∠А:

BC / AC = tangent ∠A = tangent 60 ° = √3.

BC = AC x √3 = 12 x √3 = 12√3 cm.

4. AB = √BC² + AC² = √ (12√3) ² + 12² = √144 x 3 + 144 = √576 = 24 cm.

5. BE = AB – AE = 24 – 6 = 18 cm.

Answer: BE = 18 cm, AE = 6 cm.