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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.

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 class=

Answer :

To solve this question we will use the cosine law:

[tex]c^2=a^2+b^2-2ab\cos C.[/tex]

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:

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

Therefore:

[tex]c=1105.308698\text{ ft.}[/tex]

Answer: third option.

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