# In triangle ABC, angle BAC = 90 and angle In triangle ABC, angle BAC = 90 and angle BCA = 15 degrees.

July 27, 2021 | education

| **In triangle ABC, angle BAC = 90 and angle In triangle ABC, angle BAC = 90 and angle BCA = 15 degrees. Point D is the inner melancholy of the AC segment, the angle of the internal combustion engine = 15 degrees. calculate the length of the leg AB if DC = 6cm.**

Since in the BCD triangle the angle BCD = CBD = 15, then the BCD triangle is isosceles, BD = CD = 6 cm.

Determine the value of the angle ABC. Angle ABC = (180 – 90 – 15) = 75.

Then in a right-angled triangle ABD the angle ABD = (75 – 15) = 60, then the angle ADB = (90 – 60) = 30.

Then the leg AB located opposite the angle 30 is equal to half of the hypotenuse BD.

AB = BD / 2 = 6/2 = 3 cm.

Answer: The length of the leg AB is 3 cm.

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