Find the sides and angles of an isosceles triangle if the angle at its base is 75 degrees

| January 16, 2021 | education

Find the sides and angles of an isosceles triangle if the angle at its base is 75 degrees, the perimeter is 46 cm and its base is 8 cm larger than the side.

The angles at the base are equal, which means that the angle at the top will be:
180 ° – (75 ° + 75 °) = 30 °.
We introduce the variable x and denote the length of the lateral side of this triangle, then the length of the base is (x + 8) cm.Let’s use the formula for the perimeter of a triangle and compose the equation:
x + x + x + 8 = 46
3x = 38
x = 38/3 = 12 2/3 (cm) – side;
12 2/3 + 8 = 20 2/3 (cm) – base.
The sides turned out not quite “pretty”. Possibly a typo and a 47 cm perimeter, then the equation would be:
3x = 39
x = 13 (cm) – side;
13 + 8 = 21 (cm) – base.
Answer: the angles of the triangle are 75 °, 75 °, 30 °, sides are 12 2/3 cm, 12 2/3 cm, 20 2/3 cm.



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