Question

To find the distance across a small lake, a surveyor has taken the measurements shown in the figure below. If a = 850 ft, b = 960 ft, and C = 75°, find the distance across the lake.

Answer 1

To solve this question we will use the cosine law:

`c^2=a^2+b^2-2ab\cos C.`

c is the distance we are looking for and we are given that a=850, b=960, and C=75°. Substituting those values in the above equation we get:

`\begin{gathered} c^2=(850^2+960^2-2(850)(960)\cos 75^(\circ))ft^2, \\ c^2=1221707.318ft^2. \end{gathered}`

Therefore:

`c=1105.308698\text{ ft.}`

Answer: third option.