AB and BC – lateral sides,
АС – base,
AB = 6 centimeters,
angle A = 75 degrees.
Find the area of the triangle ABC -?
Consider an isosceles triangle ABC. Its sides and angles at the base are equal to each other, that is, AB = BC = 6 centimeters and angle A = angle C = 75 degrees. Knowing that the sum of the degree measures of the triangle is 180 degrees:
angle A + angle B + angle C = 180;
angle B = 180 – angle A – angle C;
angle B = 180 – 75 – 75;
angle B = 30 degrees.
The area of the triangle ABC, that is, S ABC = 1/2 * AB * BC * sin B;
S ABC = 1/2 * 6 * 6 * 1/2;
S ABC = 1/2 * 36 * 1/2;
S ABC = 9 cm ^ 2.
Answer: 9 cm ^ 2.
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