G.8 - Right Triangles

G.8   The student will solve problems, including practical problems, involving right triangles.  This will include applying

a)  the Pythagorean Theorem and its converse;

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.
  

·  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.8a ₁  Determine whether a triangle formed with three given lengths is a right triangle.

·  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, calculate

2016 Word Wall Cards