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2 years ago

A group of Boy Scouts on a straight trail headed N30.6 E found the trail led through a briar patch. They

Mathematics

1 answer:

Svetradugi [14.3K]2 years ago

7 0

Answer:

about 113 meters

Step-by-step explanation:

If the straight-line distance is 1, then the distance around is ...

sin(30.6°) +cos(30.6°) ≈ 1.36978.

The 156 meters due east is the product of the straight-line distance and sin(30.6°), so we have ...

excess distance = (1.36978 -1)·(straight-line distance)

= 0.36978·(156 m)/sin(30.6°) = 113.3 m

The group walked about 113 meters farther to avoid the briar patch.

_____

<em>More detail</em>

The sine of an acute angle in a right triangle is the ratio of the opposite side to the hypotenuse. Here, that is ...

sin(30.6°) = (156 m)/(straight-line distance)

Multiplying by the denominator, and dividing by sin(30.6°), we get ...

(straight-line distance)·sin(30.6°) = 156 m

straight-line distance = (156 m)/sin(30.6°) . . . . . . the value used above

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