Right Triangles.

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Presentation transcript:

Right Triangles

Right Triangles A triangle with a right angle in it Scalene Right Triangle- One right angle, two other unequal angles, no equal sides Isosceles Right Triangle- One right angle, two other equal angles, two equal sides

Pythagorean Theorem In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides. Hypotenuse- the longest side of the right triangle and is always opposite of the right angle Leg(s)- the sides of the right triangle that are on either side of the right angle

Pythagorean Theorem a2 + b2 = c2 A is a leg B is a leg C is the hypotenuse

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle a2 + b2 = c2 52 + 122=c2 25 + 144 = c2 169= c2 √169 = √c2 13 =c

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle a2 + b2 = c2 122 + b2=242 144 + b2 = 576 -144 -144 b2= 432 √b2 = √432 b =√432

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle a2 + b2 = c2 72 + b2=92 49 + b2 = 81 -49 -49 b2= 32 √b2 = √32 b =√32

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle

Practice Work on the following worksheet!

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle Maria walked 3 km west and 4 km south. Calculate how far she is from her starting point. 3 km a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 √ 25 = √ c2 5 = c 4 km ? km

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle Lena’s guest house is 15 m long and 12 m wide. How long is the diagonal of the house? 12 km a2 + b2 = c2 152 + 122 = c2 225 + 144 = c2 369 = c2 √ 369 = √ c2 √ 369 = c 15 km ? km

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long. Calculate how many feet of fencing he will need to surround the entire lot. 200 ft a2 + b2 = c2 1252 + 2002 = c2 15,625 + 40,000= c2 55,625 = c2 √ 55, 625= √ c2 √ 55, 625= c 125 ft ? ft

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long. Calculate how many feet of fencing he will need to surround the entire lot. 200 ft a2 + b2 = c2 1252 + 2002 = c2 15,625 + 40,000= c2 55,625 = c2 √ 55, 625= √ c2 √ 55, 625= c 125 ft ? ft

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle A builder needs to add diagonal braces to a wall. The wall is 16 feet wide by 12 feet high. What is the length of each brace?

Pythagorean Theorem a2 + b2 = c2 We use the Pythagorean Theorem to find a missing side of a right triangle The diagram at the right shows how a post was broken. What was the original height of the post?