ACT Preparation / Unit 14 ACT 1319 worked example, 60 to 90 seconds
Choosing the Ratio
The idea
Choosing a trig ratio takes three steps. First, mark the known angle. Second, label the sides relative to it: the hypotenuse, opposite the right angle; the opposite side, facing the known angle; and the adjacent side, touching it. Third, choose the ratio that links the side you know with the side you want: opposite and hypotenuse use sine, adjacent and hypotenuse use cosine, and opposite and adjacent use tangent.
In practice
Worked example: a right triangle has a 35° angle, and the side adjacent to it is 20. Find the opposite side. Adjacent and opposite call for tangent: tan 35° = x/20, so x = 20 tan 35°, about 20 × 0.700 = 14.0. To find the hypotenuse instead: cos 35° = 20/h, so h = 20/cos 35°, about 24.4.
Where people slip
Opposite and adjacent change when the reference angle changes: the side opposite one acute angle is adjacent to the other.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
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