ACT Preparation / Unit 14 ACT 1322 worked example, 60 to 90 seconds
A Right-Triangle Trig Problem
The idea
A trigonometry word problem is solved in four steps. First, sketch the situation and find the right triangle, with its horizontal and vertical sides. Second, place the given angle, measured from the horizontal. Third, label the known side and the wanted side relative to that angle, and choose the ratio. Fourth, solve, and check that the answer's size makes sense.
In practice
Worked example: from the top of a cliff 80 meters high, a boat is seen at an angle of depression of 20°. How far is the boat from the foot of the cliff? The angle of depression equals the angle of elevation from the boat, 20°, by alternate interior angles. Opposite: 80. Adjacent: the distance d. tan 20° = 80/d, so d = 80/tan 20°, about 220 meters.
Where people slip
Put the angle of depression inside the triangle by alternate interior angles. Placing 20° at the top of the cliff, between the cliff and the line of sight, would give 80 tan 20°, about 29 meters, which is wrong.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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