Question

I WIL VOTE BRAINLISET SOMEONE PLEASE HELP

Answer 1

Answer:

  26.0 cm

Step-by-step explanation:

Given quadrilateral ABCD with diagonal BD forming triangles ABD and BCD, and angles A=90°, C=52°, ADB=35°, and CBD=52°, you want the length of CD to 3 significant figures.

Law of Sines

The law of sines tells you the relation between sides and opposite angles is ...

  a/sin(A) = b/sin(B) = c/sin(C)

This lets us write two proportions that can be solved for the measure of CD.

In triangle ABD:

  BD/sin(A) = AB/sin(D)

  BD = AB·sin(90°)/sin(35°) = 12 cm/sin(35°) ≈ 20.921 cm

In triangle BCD:

  CD/sin(B) = BD/sin(C)

  CD = BD·sin(B)/sin(C) = 20.921 cm·sin(102°)/sin(52°) ≈ 25.969 cm

The length of CD is about 26.0 cm.