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

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.




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