In an isosceles triangle ABC, the height BD is drawn to the base of the AC. The length of the height is 6.5 cm

| November 23, 2020 | education

In an isosceles triangle ABC, the height BD is drawn to the base of the AC. The length of the height is 6.5 cm, the length of the lateral side is 13 cm. Determine the angles of this triangle.

because BD is the height, therefore the angle of BDC is 90 degrees and the triangle BDC is rectangular
in triangle BDC
BD is a leg
DC is a leg
BC hypotenuse
because the leg lying opposite an angle of 30 degrees is equal to half of the hypotenuse, and in a triangle BDC the leg is equal to half of the hypotenuse (13 we divide by 2 we get 6.5), therefore the angle BCD is 30 degrees
consider the triangle ABC:
because the triangle is isosceles, the angles at the base are equal therefore the angle BAC = BCA = 30 degrees
angle ABC = 180 – (30 + 30) = 120 degrees (because the sum of the angles in a triangle is 180 degrees)
Answer: ABC = 120 degrees, BCA = 30 degrees, BAC = 30 degrees



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