Question

From a window 100 ft above the ground in building A, the top and bottom of building B are sighted so that the angels are 70 degrees and 30 degrees respectively. Find the height of building B?

Answer 1

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:

`\begin{gathered} (\sin110)/((100)/(\cos30))\text{ = }(\sin 40)/(x) \\ \text{Cross}-\text{Multipy} \\ \text{x }*\text{ sin110 }=\text{ sin40 }*115.47 \\ \text{Divide both sides by sin110} \\ \text{x = }\frac{\sin 40\text{ }*\text{ 115.47}}{\sin \text{ 110}} \\ x\text{ = 78.986} \\ x\text{ }\approx\text{ 79 ft} \end{gathered}`

The height of the building B is 79 ft