Understanding Law of Sines
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Beginner
Start here! Easy to understand
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Beginner Explanation
The Law of Sines states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant across all three sides: a/sin A = b/sin B = c/sin C. You can use it to find a missing side when you know one side and its opposite angle, plus one other angle. Example: if a = 5, A = 30°, B = 45°, then b = (5/sin 30°)·sin 45°. Common pitfall: be sure your calculator is in the correct mode (degrees vs. radians) and watch for the ambiguous case when SSA is given.
Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
Given $\angle A = 30^\circ$, $a = 5$, and $\angle B = 45^\circ$, find $b$ using the Law of Sines.
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
Imagine you're trying to determine the height of a tree from a point 50 m away. You measure an angle of elevation of 30° at your position. Assume the triangle formed by your point, the base of the tree, and the top of the tree is right-angled at the base (90°), so the remaining angle at the top is 60°.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Given a triangle where $\angle A = 60^\circ$, $\angle B = 45^\circ$, and side $c = 10$, find side $a$.
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4
Challenge Quiz
Single Choice Quiz
Advanced
If $\angle A = 120^\circ$, $a = 8$, and $\angle B = 30^\circ$, calculate the length of $b$.
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