# 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.

### BIG IDEAS

• 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

2016 VDOE Curriculum Framework - G.8 Understanding

·  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.

### ESSENTIALS

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.

### KEY VOCABULARY

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

Updated: Aug 23, 2018