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STANDARDS

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US-VA

Math

Virginia Math

Trigonometry: Triangle Trigonometry

T.TT.1

The student will determine the sine, cosine, tangent, cotangent, secant, and cosecant of the acute angles in a right triangle and use these ratios to solve for missing sides and angle measures, including application in contextual problems.

T.TT.1.a

Define and represent the six triangular trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) of an angle in a right triangle.

T.TT.1.b

Describe the relationships between side lengths in special right triangles (30°-60°-90° and 45°-45°-90°).

T.TT.1.c

Use the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines to solve contextual problems.

T.TT.1.d

Represent and solve contextual problems involving right triangles, including problems involving angles of elevation and depression.
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T.TT.2

The student will find the area of any triangle and solve for the lengths of the sides and measures of the angles in a non-right triangle using the Law of Sines and the Law of Cosines.

T.TT.2.a

Apply the Law of Sines, and the Law of Cosines, as appropriate, to find missing sides and angles in non-right triangles.

T.TT.2.b

Recognize the ambiguous case when applying the Law of Sines and the potential for two triangle solutions in some situations.
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T.TT.2.c

Solve problems that integrate the use of the Law of Sines and the Law of Cosines and the triangle area formula (Area = 1/2 𝑎𝑏 sin 𝐶, where 𝑎 and 𝑏 are triangle sides and 𝐶 is the included angle) to find the area of any triangle, including those in contextual problems.
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