Question that includes Trigonometry

Question

In the diagram, $AB = 80 cm$, $\angle ABD = 44^∘$ (Angle B), $\angle BAC = 31^∘$, $\angle DAC =37^∘$ and $\angle DBC = 36^∘$.

Calculate:

a) $BC$

b) $BD$

c) $CD$

Answer 1

Hint: Use the Law of sines

$$\dfrac{a}{\sin A} \,=\, \dfrac{b}{\sin B} \,=\, \dfrac{c}{\sin C} \,=\, k $$.
you one of the sides. You know all the angles just substitute their respective values.

Call the intersection angle as $\angle O.$ We know $\angle O=105^0,\angle A=31^0,\angle B=44^0$ and $AB=80cm$.
By the Law of sines, we have: $\dfrac{AB}{{\sin\angle O}}=k$ Now you can compute $k$. Use the value of $k$ to find the remaining lengths. If you are not allowed to use trigonometric tables then finding $\sin \angle O$ will be a difficult task. If you still do not understand then again read the wiki article and edit your question to mention what you do not understand.