Chapter 8 Section 8.1 – The Pythagorean Theorem and Its Converse Objectives: To use the Pythagorean Theorem To use the Converse of the Pythagorean Theorem

Theorem 8.1 – Pythagorean Theorem ◦In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse a b c

Pythagorean Triple -> a set of nonzero whole numbers a, b, and c that satisfy the Pythagorean equation. ◦Common triples ◦3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25

Theorem 8.2 – Converse of the Pythagorean Theorem ◦If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Theorem 8.3 ◦If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse. a b c

Theorem 8.4 ◦If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute. a b c

Homework #6 Due Tuesday (January 29) Page ◦#1 – 31 odd

Section 8.2 – Special Right Triangles Objectives: To use the properties of triangles To use the properties of triangles

45° s s

30° 60° 2s s

Ex: What is the value of x? 45° x 6

Ex: Find the value of each variable. 60° 30° d f 5

Homework #7 Due Wed/Thurs (Jan 30/31) Page #428 ◦# 1 – 22 all

Section 8.3 – The Tangent Ratio Objectives: To use tangent ratios to determine side lengths in triangles

Ex: Find the tangent ratios for each angle. T U V Tan U = ? Tan T = ?

Ex: Find the value of each variable 10 54° w w 28° 1.0

Section 8.4 – Sine and Cosine Ratios Objectives: To use sine and cosine to determine side lengths in triangles

AC B hypotenuse Adjacent leg Opposite leg

Ex: Use the triangle to write each ratio. T G R sin T = ?cos T = ? sin G = ?cos G = ?

Homework #8 Due Friday (February 01) Page ◦#1 – 20 all Homework #9 Due Friday (February 01) Page 441 ◦#1 – 16 all Quiz Monday (8.1 – 8.4)

Section 8.5 – Angles of Elevation and Depression Objectives: To use angles of elevation and depression to solve problems

38° Horizontal Line Angle of Depression Angle of Elevation A person looking up at a hot air balloon at a 38 degree angle. This is the angle of elevation. Person in the hot air balloon looking down at the person on the ground at a 38 degree angle. This is the angle of depression.

You sight a rock climber on a cliff at a 32° angle of elevation. The horizontal ground distance to the cliff is 1000 ft. Find the line-of-sight distance to the rock climber. Person Climber 1000 ft 32° x

A rescue helicopter pilot sights a life raft at a 26° angle of depression. The helicopter’s altitude is 3km. What is the helicopter’s surface distance (d) from the raft? Raft Helicopter 26° 3km d

Homework #10 Due Thurs/Fri (Feb 06/07) Page 447 ◦#1 – 14 all

Section Vectors Objectives: To describe vectors To solve problems that involve vector addition

Vector -> any quantity with magnitude (size) and direction. Vectors are notated with Ex: KW The magnitude corresponds to the distance from initial point K to the terminal point W. The direction corresponds to the direction in which the arrow points.

Ex: Describe OL as an ordered pair. Give the coordinates to the nearest tenth. O x y 50° 65 L

Ex: Describing a Vector Direction ◦Use compass directions to described the direction of each vector. N E S W 25° N E S W 35°

Ex: A small airplane lands at a point 246 mi east and 76 mi north of the point from which it took off. Describe the magnitude and the direction of its flight vector.

Homework #11 Due Tuesday (Feb 12) Page ◦#1 – 12 all ◦#14 – 24 even Chapter 8 Test Thurs/Fri