Let's begin solving the problem by illustrating the problem using a diagram:
Let the height of building B be x
Re-drawing the triangles to show the unknown side:
Using trigonometric ratios and sine rule
Hence:
[tex]\begin{gathered} \frac{\sin110}{\frac{100}{\cos30}}\text{ = }\frac{\sin 40}{x} \\ \text{Cross}-\text{Multipy} \\ \text{x }\times\text{ sin110 }=\text{ sin40 }\times115.47 \\ \text{Divide both sides by sin110} \\ \text{x = }\frac{\sin 40\text{ }\times\text{ 115.47}}{\sin \text{ 110}} \\ x\text{ = 78.986} \\ x\text{ }\approx\text{ 79 ft} \end{gathered}[/tex]
The height of the building B is 79 ft
