In triangle ABC, angle C is straight, AB = 2cm, angle B is 60 degrees

| August 11, 2021 | education

In triangle ABC, angle C is straight, AB = 2cm, angle B is 60 degrees, MC is perpendicular to the plane ABC, MC = 2cm. Find the area of the triangle AMB.

In a right-angled triangle ABC, the angle BAC = 90 – 60 = 30.

Then the leg BC is located opposite the angle 30, and therefore, the length of the leg BC = AB / 2 = 2/2 = 1 cm.

Let’s build the height CH of the right-angled triangle ABC.

In a right-angled triangle BCH, we determine the length of the CH leg.

Then Sin60 = CH / BC.

CH = BC * Sin60 = 1 * √3 / 2 cm.

In the right-angled triangle MCH, we determine the length of the hypotenuse MH.

MH ^ 2 = MC ^ 2 + CH ^ 2 = 4 + 3/4 = 19/4.

MH = √19 / 2 cm.

Determine the area of the triangle AMB.

Samv = AB * MN / 2 = 2 * (√19 / 2) / 2 = √19 / 2 cm2.

Answer: The area of the AMB triangle is √19 / 2 cm2.



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