The sail of a boat is in the shape of a right triangle, as shown below: which expression shows the length, in meters, of the base of the sail? (6 points) 7 cosec 50° 7 divided by sec 50 degrees 7 divided by cosec 50 degrees 7 cot 50°

Choice C
7 divided by cosec 50 degrees



Explanation:

Abbreviations:
sec = secant
cot = cotangent
cosec = cosecant (csc is also a widely used abbreviation)



Let the horizontal leg be x

This leg is opposite the angle 50 degrees. The hypotenuse is 7

Opposite = x
Hypotenuse = 7

We'll either use the sine rule or the cosecant (csc) rule
sine = opposite/hypotenuse
cosecant = hypotenuse/opposite

Since "sine" is nowhere to be found in the answer choices, we'll use the cosecant rule



cosecant = hypotenuse/opposite
csc(angle) = hypotenuse/opposite
csc(50) = 7/x
x*csc(50) = 7
x = 7/csc(50)

This is why the answer is choice C