Find a leg of a right-angled triangle lying opposite an angle of 60 degrees if its hypotenuse is 8 m.
June 15, 2021 | education
| Given:
right-angled triangle ABC;
angle C = 90 degrees;
angle B = 60 degrees;
AB – hypotenuse,
AB = 8 meters.
Find the length of the AC leg -?
Decision:
Consider a right-angled triangle ABC.
Angle A = 180 – angle B – angle C;
angle A = 180 – 60 – 90;
angle A = 60 degrees.
In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then BC = 1/2 * AB = 1/2 * 8 = 4 (meters).
By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AC ^ 2 + BC ^ 2 = AB ^ 2;
AC ^ 2 = AB ^ 2 – BC ^ 2;
AC ^ 2 = 64 – 16;
AC ^ 2 = 48;
AC = 4√3 meters.
Answer: 4√3 meters.
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