Mississippi Math G-SRT.8

MathGrades 9–12Congruence

The Standard

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems and rewrite expressions involving radicals to simplify and interpret solutions. *

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Define Trigonometric Ratios and Solve Problems involving Right Triangles

Teacher's field guide

What This Standard Means

What Students Need to Do: Students sketch and label a right triangle from a real situation. They use sine, cosine, tangent, or the Pythagorean Theorem to find missing sides and angles. They simplify radicals and report measurements with units.
What Mastery Looks Like: A student identifies the opposite side, adjacent side, and hypotenuse for the angle they are using. They choose a method that fits the known measurements, simplify √72 to 6√2, and round when the situation calls for an estimate.
Common Misconceptions: Students may think opposite and adjacent name fixed sides, even when the marked angle changes. They may add squares instead of subtracting when finding a leg, or treat an exact radical answer as a rounded measurement.
How to Assess It: Exit ticket: A cable reaches a pole from a point 6 feet away at a 45° angle to the ground. Find the pole height with tangent, then use the Pythagorean Theorem to find the cable length as a simplified radical. Label both lengths.

Lesson moves

Ways to Teach It

Build a straw clinometer, measure the angle to a tree top and your distance from its base, then calculate height including eye level.
Ask students why a ladder reaching 10 feet up a wall from 5 feet away has length 5√5 feet, not 15 feet.
Give pairs right-triangle cards with one missing measure; partners match each card to sine, cosine, tangent, or the Pythagorean Theorem.
Give students a loading ramp plan with a 30-inch rise and a 12° incline; have them find the ramp length to the nearest inch.

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