precal question

Question

For the triangle shown, find the following. (Assume u = v = 25 and w = 30. Round your answers to one decimal place.)

(a)     ∠BCD

 °

(b)     ∠DCA

 °

Answer 1

By the law of sines:

sine <CDA/30 = sin 30 /25

since 180 degrees total for interior angles of a triangle, m<DCA = 180 - m<CDA - 30

<CDA and <CDB are a linear pair, so m<CDB = 180 - m<CDA

since u = v, triangle BCD is isosceles and m<CBD = m<CDB

since 180 degrees total for interior angle of a triangle, m<BCD = 180 = m<CBD - m<CDB

Answer 2

Just by looking at this triangle; it's an isocolies; 2=sides. In this case there's 3=sides; so there's 3=angles; 60° each.

As for dca we've got to subtract the 2 other angles from 180°.

D=180-60=120. dca=180-120-30=30°.

Answer 3

sin ∠CDA / 30 = sin 30º / 25

Then determine m∠CDB, then m∠CBD, then m∠BAD

Then determine m ∠DCA