Calculate the area of an isosceles triangle if the angle at the base is 75 degrees and its lateral side is 6cm.

Given:

triangle ABC,

AB and BC – lateral sides,

АС – base,

AB = 6 centimeters,

angle A = 75 degrees.

Find the area of ​​the triangle ABC -?

Solution:

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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