In the right-angled triangle ABC, the height CH is drawn. It is known that the angle CAB = 60 degrees, and AB = 25cm.

| December 16, 2020 | education

In the right-angled triangle ABC, the height CH is drawn. It is known that the angle CAB = 60 degrees, and AB = 25cm. Find what the AC side and the НВС angle and the НВС angle are equal to.

We will use the properties of a right-angled triangle. (Constructed drawing) Angle ABC + angle CAB = 90 °. => Angle ABC = 90-60 = 30 ° (the sum of acute angles in a right-angled triangle) AC is a leg opposite an angle of 30 degrees. By the property of a right-angled triangle, it is equal to half the hypotenuse. Hypotenuse AB. She is 25cm. AC = 25: 2 = 12.5cm. Next, we consider СНВ right-angled triangle. (it is rectangular, since CH is the height) If the angle ABC = 30 °, then the angle HCB = 90 ° -30 ° = 60 °. (by the property of a right-angled triangle) Answer: AC = 12.5 cm., angle НВС (aka ABC) = 30 °, angle HCB = 60 °.



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