They spend much more time on indirect measurement techniques than they did in earlier grades, expanding their repertoire to include not only the use of proportions and similarity but also the use of the Pythagorean Theorem and basic right triangle trigonometric relationships. Students at the high school level will frequently use measurement to help develop connections to other mathematical concepts. For example, students may use a computer program that measures angles to help them discover the relationship between the measures of two vertical angles formed by intersecting lines or the measures of inscribed angles intercepting the same arc of a circle. They may also develop algebraic techniques to help them find measures, as, for example, when they develop a formula for finding the distance between two points in the coordinate plane. High school students also use measurement frequently in connection with other subject areas.
Science experiments require a precise use of measurement.
The cumulative progress indicators for grade 12 appear below in boldface type. Use techniques of algebra, geometry, and trigonometry to measure quantities indirectly. Students use coordinate geometry techniques to determine the distance between two points. Students use similar figures and proportions to measure the height of a tree or a flagpole. Students use the Pythagorean Theorem to determine how long a ladder is needed to climb a wall, including a determination of a safe angle at which to place the ladder.