In a right-angled triangle ABC with a hypotenuse AB, the height CD is drawn, the angle B is 60 °
| June 20, 2021 | education
In a right-angled triangle ABC with a hypotenuse AB, the height CD is drawn, the angle B is 60 °, the segment BD = 1 cm. Find the length of the hypotenuse AB.
Since CD is height, triangle CDB is right-angled.
Since angle D is right and angle B is 60 °, then angle BCD = 180 ° – 90 ° – 60 ° = 30 °.
In a right-angled triangle, the leg against an angle of 30 ° is equal to half the hypotenuse. Therefore, the hypotenuse BC = 2 * BD = 2 cm.
Consider a right-angled triangle ABC:
Since angle C is right and angle B is 60 °, then angle BAC = 180 ° – 90 ° – 60 ° = 30 °.
In a right-angled triangle, the leg against an angle of 30 ° is equal to half the hypotenuse. Therefore, the hypotenuse AB = 2 * BC = 2 * 2 cm = 4 cm.
Answer: 4 cm.
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