Becky Afghani, LBUSD Math Curriculum Office, 2004 Right Triangles

Becky Afghani, LBUSD Math Curriculum Office, 2004 TEKS P.3 Precalculus/Knowledge and Skills. The student uses functions and their properties, tools and technology, to model and solve meaningful problems. The student is expected to: P.3A Investigate properties of trigonometric and polynomial functions. P.3E Solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

Becky Afghani, LBUSD Math Curriculum Office, 2004 Lesson Synopsis: Students review their basic understandings of trigonometry by using sine, cosine, tangent, and the Pythagorean Theorem to solve a variety of right triangle problems.

Becky Afghani, LBUSD Math Curriculum Office, 2004 Vocabulary Right Triangle Legs Hypotenuse Pythagorean Theorem Triangle Triangle

Becky Afghani, LBUSD Math Curriculum Office, 2004 What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse. leg hypotenuse right angle

Becky Afghani, LBUSD Math Curriculum Office, 2004 The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a 2 + b 2 = c 2. Note: The hypotenuse, c, is always the longest side.

Becky Afghani, LBUSD Math Curriculum Office, 2004 Find the length of the hypotenuse if 1. a = 12 and b = = c = c = c 2 Take the square root of both sides. 20 = c

Becky Afghani, LBUSD Math Curriculum Office, 2004 Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = b 2 = b 2 = 100 Solve for b b 2 = b 2 = 84 b = 9.17

Becky Afghani, LBUSD Math Curriculum Office, 2004 Find the length of the missing side given a = 4 and c =

Becky Afghani, LBUSD Math Curriculum Office, 2004 Pythagorean Triples

Becky Afghani, LBUSD Math Curriculum Office, 2004 What are Pythagorean Triples? Three integers that make the equation a 2 + b 2 = c 2 true are called Pythagorean Triples. The numbers 3, 4 and 5 are a very famous Pythagorean Triple. a 2 + b 2 = c = = 25

Becky Afghani, LBUSD Math Curriculum Office, 2004 Why Memorize Pythagorean Triples? Remember how much time it took to figure out 8 x 8 before you memorized it? ( = 64) Think of all the work involved to solve this problem: a 2 + b 2 = c = x = x 2 25 = x 2 5 = x Wouldn ’ t it be nice to just know this is 5?

Becky Afghani, LBUSD Math Curriculum Office, 2004 Good Pythagorean Triples to Memorize: And multiples of each, like: 3x2, 4x2, 5x

Becky Afghani, LBUSD Math Curriculum Office, 2004 Directions: The following slides show common Pythagorean Triples. It is faster to recognize these triples on sight than to apply the Pythagorean Theorem. When the right triangle appears, SAY ALOUD the length of the missing side. Try to beat the computer by saying the answer BEFORE it appears in 8 seconds.

Becky Afghani, LBUSD Math Curriculum Office, 2004

x 2

Becky Afghani, LBUSD Math Curriculum Office, 2004

x 10

Becky Afghani, LBUSD Math Curriculum Office, 2004

x 6

Becky Afghani, LBUSD Math Curriculum Office, 2004 Way to Go!!

Becky Afghani, LBUSD Math Curriculum Office, 2004 Lesson 7-3: Special Right Triangles30 Special Right Triangles

Becky Afghani, LBUSD Math Curriculum Office, 2004 Lesson 7-3: Special Right Triangles 31 45°-45°-90° Special Right Triangle In a triangle 45°-45°-90°, the hypotenuse is times as long as a leg. 45° Hypotenuse X X X Leg Example: 45° 5 cm 5 cm

Becky Afghani, LBUSD Math Curriculum Office, 2004 Lesson 7-3: Special Right Triangles 32 30°-60°-90° Special Right Triangle In a triangle 30°-60°-90°, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg. 30° 60° Hypotenuse X 2X X Longer Leg Shorter Leg Example: 30° 60° 10 cm 5 cm

Becky Afghani, LBUSD Math Curriculum Office, 2004 Lesson 7-3: Special Right Triangles 33 Example: Find the value of a and b. 60° 7 cm a b Step 1: Find the missing angle measure.30° Step 2: Decide which special right triangle applies.30°-60°-90° Step 3: Match the 30°-60°-90° pattern with the problem. 30° 60° x 2x a = cm b = 14 cm Step 5: Solve for a and b Step 4: From the pattern, we know that x = 7, b = 2x, and a = x.

Becky Afghani, LBUSD Math Curriculum Office, 2004 Lesson 7-3: Special Right Triangles 34 Example: Find the value of a and b. 45° 7 cm a b Step 1: Find the missing angle measure.45° Step 2: Decide which special right triangle applies.45°-45°-90° Step 3: Match the 45°-45°-90° pattern with the problem. 45° x x x Step 4: From the pattern, we know that x = 7, a = x, and b = x. a = 7 cm b = 7 cm Step 5: Solve for a and b

Becky Afghani, LBUSD Math Curriculum Office, 2004 Time for you to practice! Get out your phones! Go to the Class Website and complete your e-worksheet! Due Fri Nov 7 (A Day) Due Mon Nov 11 (B Day)