An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

To find the measure of angle ∠ B A C in the right triangle ABC, we can use trigonometric ratios. Since ∠ A CB is the right angle, this triangle's configuration allows us to apply sine, cosine, and tangent functions.
Given:

Hypotenuse A B = 12 cm
Opposite side to ∠ B A C is A C = 6.9 cm
Adjacent side to ∠ B A C is CB = 9.8 cm

To find m ∠ B A C , the following trigonometric expressions can be used:

Using cosine: cos − 1 ( A B A C ​ ) = cos − 1 ( 12 6.9 ​ ) This expression gives m ∠ B A C because cosine of angle BAC is the ratio of the adjacent side (AC) to the hypotenuse (AB).

Using sine: sin − 1 ( A B A C ​ ) = sin − 1 ( 12 6.9 ​ ) This expression is incorrect because it is based on the opposite side, not adjacent.

Using tangent: tan − 1 ( CB A C ​ ) = tan − 1 ( 9.8 6.9 ​ ) This expression correctly calculates m ∠ B A C since tangent of angle BAC is the ratio of the opposite side (AC) to the adjacent side (CB).


So, the correct expressions to find m ∠ B A C are:

cos − 1 ( 12 6.9 ​ )
cos − 1 ( 12 9.8 ​ )
tan − 1 ( 9.8 6.9 ​ )

When selecting options from the multiple-choice list provided by the student, it would be:

cos − 1 ( 12 6.9 ​ )
tan − 1 ( 9.8 6.9 ​ )

Answered by MasonWilliamTurner | 2025-07-21

In 30 seconds, an electric device delivering 15.0 A of current allows approximately 2.81 x 10^21 electrons to flow through it. This calculation involves determining the total charge passed using the relationship between current, charge, and time. Finally, this charge is divided by the charge of a single electron to find the total number of electrons.
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Answered by MasonWilliamTurner | 2025-07-23