Math - 2018-19
G.8bc - Special Right Triangles and Trig
G.8 The student will solve problems, including practical problems, involving right triangles. This will include applying
b) properties of special right triangles;
c) trigonometric ratios.
- I can determine what size TV to purchase, figure what length
ladder will be needed for a job, and find the shortest route to travel.
- I will calculate the length of a segment and determine a right
angle without directly measuring.
UNDERSTANDING THE STANDARD
· The converse of the Pythagorean Theorem can be used to determine if a triangle is a right triangle.
· 45°-45°-90° and 30°-60°-90° triangles are special right triangles because their side lengths can be specified as exact values using radicals rather than decimal approximations.
· The sine of an acute angle in a right triangle is equal to the cosine of its complement.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
· G.8b1 Solve for missing lengths in geometric figures, using properties of 45°-45°-90° triangles where rationalizing denominators may be necessary.
· G.8b2 Solve
for missing lengths in geometric figures, using properties of 30°-60°-90° triangles where
rationalizing denominators may be necessary.
· G.8c1 Solve
problems, including practical problems, involving right triangles with missing
side lengths or angle measurements, using sine, cosine, and tangent ratios.
· G.8abc1 Solve
problems, including practical problems, using right triangle trigonometry and
properties of special right triangles.
triangle, side, angle, right angle, right
triangle, Pythagorean Theorem, Converse of Pythagorean Theorem, special right
triangle, right triangle trigonometry, length, geometric figure, 45°-45°-90° triangle, 30°-60°-90° triangle, sine, cosine, tangent, grade, hypotenuse, short leg, long
leg, complementary angle, angle of elevation, angle of depression, ratio,
similar, adjacent, adjacent side, opposite, opposite, scale factor, justify,