The picture below shows a box sliding down a ramp: a right triangle abc has measure of angle abc equal to 90 degrees and measure of angle acb equal to 70 degrees. the length of ab is 20 feet. what is the distance, in feet, that the box has to travel to move from point a to point c? 20 cosec 70° 20 divided by cot 70 degrees 20 divided by sec 70 degrees 20 sin 70°

ac is the hypotenuse of the triangle. ab is the side opposite ∠c. the trig ratio that relates the opposite side to the hypotenuse is the sine.

sin(∠c) = opposite/hypotenuse = (ab)/(ac)

solving this for ac gives

ac = ab/sin(∠c) = ab×csc(∠c) . . . using the relation csc = 1/sin

substituting the given numbers, this becomes

ac = 20×csc(70°) . . . matches the first selection

the answer you are looking for is 20 cosec70

b

step-by-step explanation:

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