Question

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°

Answer 1

the answer is C.

Explanation:

Answer 2

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

`sin60^(\circ)=(AC)/(AB)\\\\\Rightarrow\ AB=ACsin60^(\circ)\\\Rightarrow\ AB=0.5\ sin60^(\circ)`

Now Distance towards west
`AD=|\ -0.5\ sin60^(\circ)|` [distance is a positive quantity]

`AD=0.5\ sin60^(\circ)`

`AD=0.5\ cos(90^(\circ)-60^(\circ))` [Taking complementary angle of 60° ]

`AD=0.5\ cos(30^(\circ))`

Thus C. is the right option.