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You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake.

Which of the following expressions uses the complementary angle of 60° to determine how far you would travel on your trip west?
a.
0.5cos30°
b.
0.5cos60°
c.
0.5sin30°
d.
0.5sin60°

Respuesta :

JeanaShupp

Answer:- c. 0.5sin30°


Explanation:-

Let AB= 0.5 miles be the distance across the lake to 60º north of east.

AC= distance travel to the east

Now, in right ΔABC

[tex]sin60^{\circ}=\frac{AC}{AB}\\\\\Rightarrow\ AB=ACsin60^{\circ}\\\Rightarrow\ AB=0.5\ sin60^{\circ}[/tex]

Now Distance towards west  [tex]AD=|\ -0.5\ sin60^{\circ}|[/tex] [distance is a positive quantity]

[tex]AD=0.5\ sin60^{\circ}[/tex]

[tex]AD=0.5\ cos(90^{\circ}-60^{\circ})[/tex]  [Taking complementary angle of 60° ]

[tex]AD=0.5\ cos(30^{\circ})[/tex]

Thus C. is the right option.

Ver imagen JeanaShupp
bh3896

Answer:

the answer is C.

Step-by-step explanation:

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