Given a right-angled triangle ABC, angle C of a straight line. It is known that AC = 6. Find meliana CM if tg B = 3/4
| June 30, 2021 | education
Since the angle ACB is 90, the triangle ABC is rectangular.
The tangent of an acute angle of a right-angled triangle is equal to the ratio of the length of the opposite leg to the length of the adjacent leg.
tgABC = AC / BC.
BC = AC / tgABC = 6 / (3/4) = 8 cm.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 36 + 64 = 100.
AB = 10 cm.
In a right-angled triangle, the median drawn to the hypotenuse is half its length. CM = AB / 2 = 10/2 = 5 cm.
Answer: The length of the median CM is 5 cm.
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