In triangle ABC, the angle b is equal to 120 degrees. Find the side AB if the height an is 9 cm.
July 29, 2021 | education|
In the ABC triangle it is known:
Angle B = 120 °;
Height BH = 9 cm.
Let’s find the AB side.
Consider a triangle ABH with a right angle H.
Angle B = 120 ° / 2 = 60 °;
Then the angle A = 30 °.
It is known that BH = 9 cm.
Then we find the side AB.
sin A = BH / AB;
From here we express BН.
AB = BH / sin A;
Substitute the known values and calculate the AB side.
AB = 9 / sin 30 = 9 / (1/2) = 9 * 2/1 = 9 * 2 = 18;
As a result, we got that the side AB of the triangle ABC is 18 cm.
Answer: AB = 18 cm.
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