Montana Math MT.PLUS.ALG.TRIG.5

MathGrades 9–12Trigonometric Functions

The Standard

Apply the Law of Sines and the Law of Cosines to find unknown measurements in non-right triangles.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students use known sides and angles to choose the Law of Sines or Law of Cosines. They find a missing side or angle in a triangle without a right angle.
What Mastery Looks Like: A student picks the right rule and calculates a missing measurement. With two sides and a nonincluded angle, they check whether a second triangle is possible.
Common Misconceptions: Students use right-triangle sine and cosine ratios on triangles without right angles. They may pair a side with the wrong opposite angle or assume their calculator's inverse sine result is the only possible angle.
How to Assess It: Exit ticket: A triangle has sides of 6 cm and 9 cm with a 60° angle between them. Find the third side and name the rule you used.

Lesson moves

Draw a triangle with 5 cm and 7 cm sides meeting at 60°, measure the third side, then check it with the Law of Cosines.
Ask pairs: “Two sides and the angle between them are given. Which rule finds the third side, and why?”
Teams race to solve two cards: sides 5, 7, included angle 60°; angles 40°, 70°, side 8 opposite 40°.
Use a map with two 100 m trails meeting at 40° to calculate the straight-line distance between their endpoints.

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