#### Math - 2019-20

# G.8 - Right Triangles

G.8The student willsolveproblems, including practical problems, involving right triangles. This will includeapplyinga) the Pythagorean Theorem and its converse;

b) properties of special right triangles;

c) trigonometric ratios.

*Adopted: 2016*

### 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

· 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.8a _{1} **Determine** whether a triangle formed with three given lengths is a right triangle.

· G.8b_{1} **Solve**
for missing lengths in geometric figures, using properties of 45°-45°-90° triangles where
rationalizing denominators may be necessary.

· G.8b_{2} **Solve**
for missing lengths in geometric figures, using properties of 30°-60°-90° triangles where
rationalizing denominators may be necessary.

· G.8c_{1} **Solve**
problems, including practical problems, involving right triangles with missing
side lengths or angle measurements, using sine, cosine, and tangent ratios.

· G.8abc_{1} **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: Jul 30, 2019*