In a right-angled triangle, the hypotenuse is 10 cm, and the acute angle is 30 degrees. Find the leg adjacent to the given corner.
| July 18, 2021 | education
In a right-angled triangle, the leg, opposite an angle of 30 °, is equal to half the hypotenuse. Therefore, AC = ½ BC = ½ * 10 = 5 (cm).
By the Pythagorean theorem, BC ^ 2 = AC ^ 2 + BA ^ 2.
BA ^ 2 = BC ^ 2 – AC ^ 2 = 10 ^ 2 – 5 ^ 2 = 100 – 25 = 75.
BA = √75 = 5√3 (cm).
Answer: the leg adjacent to the angle of 30 ° is 5√3 cm.
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