Math Problem Solver

A basic highway curve connecting two straight sections of road is often circular.In the​ figure, the points P and S mark the beginning and end of the curve. Let Q be the point of intersection where the two straight sections of highway leading into the curve would meet if extended. The radius of the curve is​ R, and the central angle denotes how many degrees the curve turns.

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Part 1

If Requals966 ft and thetaequals37degrees​, find the distance d between P and Q.

The distance between P and​ Q, denoted as​ d, is

323.2 ft.

​(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as​ needed.)

Part 2

Choose an expression in terms of R and theta for the distance between M and N below.

A.Upper R left parenthesis 1 plus cosine StartFraction theta Over 2 EndFraction right parenthesis

Upper R left parenthesis 1 plus cosine StartFraction theta Over 2 EndFraction right parenthesis

B.Upper R left parenthesis 1 minus sine StartFraction theta Over 2 EndFraction right parenthesis

Upper R left parenthesis 1 minus sine StartFraction theta Over 2 EndFraction right parenthesis

C.Upper R left parenthesis 1 minus cosine StartFraction theta Over 2 EndFraction right parenthesis

Upper R left parenthesis 1 minus cosine StartFraction theta Over 2 EndFraction right parenthesis

D.Upper R left parenthesis 1 plus sine StartFraction theta Over 2 EndFraction right parenthesis

Upper R left parenthesis 1 plus sine StartFraction theta Over 2 EndFraction right parenthesis