In triangle ABC, angle C is 90 ‘, CH is height, AB = 27, sin A = 2/3. Find BH.
July 27, 2021 | education|
In triangle ABC it is known:
Angle C is 90 °;
AB = 27;
sin a = 2/3.
1) If sin a and AB are known, then we can find BC.
sin a = BC / AB (ratio of the opposite leg to the hypotenuse);
Hence, BC = AB * sin a;
Substitute the known values.
BC = 27 * 2/3 = 27/3 * 2 = 9 * 2 = 18;
2) Since, sin a = cos b, then cos b = 2/3;
3) Consider a triangle CHB, where the angle H = 90 °.
cos b = BH / BC;
BH = BC * cos b;
BH = 18 * 2/3 = 18/3 * 2 = 6 * 3 = 12;
Hence, BH = 12.
Answer: BH = 12.
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