# Trigonometric Ratios TSOU LI LING SHANNON 2S
Get Started. It's Free Trigonometric Ratios ## 2. History

### 2.1. Pythagoras (570-495 BC): Ionian and Greek philosopher

2.1.1. Although the theorem is known as Pythagoras', when authors Plutarch and Cicero attributed the theorem to Pythagoras, they did so in a way that suggests that the attribution was widely known and undoubted.

2.1.2. Pythagoras' theorem: He studied right-angled triangles and found that the two shorter sides of the triangle squared and then added together equal the square of the longer side (hypotenuse).

## 5. Converse

### 5.2. A corollary of the Pythagorean theorem's converse is allows one to utilise the converse to determine whether a triangle is right, obtuse, or acute, as follows. Let c be chosen to be the longest of the three sides and a + b > c. The following statements apply:

5.2.1. If a2+b2=c2, then the triangle is right.

5.2.2. If a2+b2>c2, then the triangle is acute.

5.2.3. If a2+b2<c2, then the triangle is obtuse.

## 6. Applications

### 6.1. Clinometer

6.1.1. A clinometer is used to measure an object's angle of elevation from the ground in a right-angled triangle. This value, when paired with the distance from the object, can then be used to calculate the height of elevation. This is especially useful when the object is too high to be measured easily.

6.1.1.1. The height of the object can be calculated using the concept of trigonometric ratios

6.1.1.1.1. Light near pool - angle of elevation: 11 degrees - distance: 5.8m

6.1.1.1.2. Clock - angle of elevation: 9 degrees - distance: 2.2m

6.1.1.1.3. Top right corner of vitamin water refrigerator - angle of elevation: 22 degrees - distance: 1.4m