Question

What is the length of AB if ∅=18° and BC=41? round to the nearest hundredth

Answer 1

First,

Name each side of the triangle

side facing right angle is the hypotanuse

side facing given angle is the opposite

the last side is the adjacent

Opposite = 41

Hypotanuse = AB

`\theta\text{ = 18}`

`\begin{gathered} \sin \theta\text{ = }\frac{opposite}{\text{hypotanuse}} \\ \sin 18\text{ = }(41)/(AB) \\ 0.309\text{ = }(41)/(AB) \\ \text{Cross multiply} \\ 0.309AB\text{ = 41} \\ \text{Divide through by 0.309} \\ AB\text{ = }(41)/(0.309) \\ AB\text{ = 132.68} \end{gathered}`