ACT Math : How to find the sine of a missing side

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #91 : Trigonometry

In the triangle below,  units and  units. What is ?



Possible Answers:

Correct answer:


Because , we need to first find the length of BC.


Using the Pythagorean theorem, 



Example Question #92 : Trigonometry


What is the value of  in the triangle above? Round to the nearest hundredth.

Possible Answers:

Correct answer:


We know that the sine of an angle is:

Therefore, we can write for this question:

This allows us to solve for  easily:

Rounding, this gives us .

Example Question #41 : Sine

A right triangle has leg lengths  and . What is the sine of the angle opposite from the side of length ?

Possible Answers:

Correct answer:


Using SOHCAHTOA, the sine of an angle is simply the length of the side opposite to it over the hypotenuse; however, we do not have the length of the hypotenuse yet.

Using the Pythagorean Theorem, we can solve for it:

So, the sine of this angle is:

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