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Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Solving Triangles
Trigonometric problem solving culminates in this chapter. Leave no side and no angle unmeasured!
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
If triangle \(ABC\) has side lengths \(a=7\), \(b=12\) and \(c=11\), the value of \( \cos A\) can be expressed as \(\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. What is the value of \(p+q\)?
Details and assumptions
\(a\), \(b\) and \(c\) are the lengths of the sides opposite to the vertices \(A\), \(B\) and \(C\), respectively.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
In a triangle, an angle of \(60^\circ\) is formed by two sides of lengths \(4\) and \(11\). If the length of the remaining side is \(\sqrt{a}\), what is \(a\)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
If parallelogram \(ABCD\) has \(\overline{AB}=8\), \(\overline{BC}=4 \) and \(\angle ABC=60^{\circ}\), what is the square of the length of the diagonal \(\overline{BD}\)?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(ABC\) be a triangle such that \(\angle A = 30^{\circ} \), \( a = 9 \sqrt{3} \) and \( c = 18 \sqrt{3} \). What is the value of \(b\)?
Details and assumptions
\(a\), \(b\) and \(c\) are the lengths of the sides opposite to the vertices \(A\), \(B\) and \(C\), respectively.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
If triangle \(ABC\) has \( \angle A = 45^{\circ}\), \(b=28\) and \(c=\sqrt{6}+14\sqrt{2}\), what is the value of \(a^2\)?
Details and assumptions
\(a\), \(b\) and \(c\) are the lengths of the sides opposite to the vertices \(A\), \(B\) and \(C\), respectively.