Chpt 10 - Trigonometry with handwritten notes

Pythagoras’s Theorem and Trigonometry Mathematics Preparatory Course for Direct Entry to Higher Nitec 10-1 Chapter 10 10.1 Introduction The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that: "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides." 10.2 Pythagoras’ Theorem In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides, i.e. 222cab= + a c b

Pythagoras’s Theorem and Trigonometry Mathematics Preparatory Course for Direct Entry to Higher Nitec 10-2 10.3 Pythagoras’ Theorem in Three Dimensions A three-dimensional object can be described by three measurements - length, width and height. We can use Pythagoras' Theorem to find the length of the longest straw that will fit inside the box or cylinder. Example 1 A can of drink is in the shape of a cylinder with height 15 cm and radius 4 cm. What is the length of the longest straw that will fit inside the can? 10.4 Pythagorean Triples A Pythagorean triple is a set of three numbers a, b and c such that Example 2 Determine whether the numbers 6, 8 and 10 form a Pythagorean triple.

Pythagoras’s Theorem and Trigonometry Mathematics Preparatory Course for Direct Entry to Higher Nitec 10-3 10.5 Trigonometric Ratios For the angle θ in a right-angled triangle as shown, we name the sides as: • hypotenuse (the side opposite the right angle) • adjacent (the side "next to" θ) • opposite (the side furthest from the angle) We define the three trigonometrical ratios sine θ, cosine θ, and tangent θ as follows: To remember these, many people use TOA, CAH, SOH. Example 3 Find the length of the side marked x. 35 cm x 33°

Pythagoras’s Theorem and Trigonometry Mathematics Preparatory Course for Direct Entry to Higher Nitec 10-4 Example 4 Find the size of angle marked θ. 10.6 Angle of elevation: In surveying, the angle of elevation is the angle from the horizontal looking up to some object: 10.7 Angle of depression: The angle of depression is the angle from the horizontal looking down to some object: Example 5 The angle of elevation of an aeroplane