## Trigonometry

#### Trigonometry: Introduction to Pythagorean Theorem

As introduced in the earlier lessons, trigonometry is the study of angles and angular relationships of triangular
objects with a 90 degree angle.

In this lesson, we'll focus on the Pythagoras theorem. The theorem states that the square on the hypotenuse
is equal to the sum of the squares on the other two sides - is well known. The equation is written below:

c = the hypotenuse

a and b = sides

There are many applications for the famous theorem. Introducing real life examples will help the students understand its
importance as well as set the stage for its day to day uses. It is always easier to learn a new concept if we can relate to it.

For example,

Three construction workers are assigned the task to lay out concrete footings for a new building in the main street.
The dimensions of the two sides adjacent and opposite to the right angled corner is 25 x 35.7 m respectively.
Find the length of the rafter needed to make the roofing.

In this case, the rafter is the hypotenuse (the longest side). Look at the picture below:

Since a = 25 and b = 35.7, we can use the Pythagorean formula to find the longest side.

C2 = (252) + (35.72)

C = 44 m

#### Try these questions:

1. The height to a third story window is 12 m, and Bob, the window cleaner needs to put a ladder 14 feet away from
the house in order to avoid the grass. What is the length of the ladder that Bob needs in order to achieve this task?

Explanation:

Convert m to ft.

(1 ft / 0.305 m) = (x / 12m)

X = 12 / 0.305

X = 39.34 ft

(39.34)2 + (14)2 = c2 (the length of ladder)

1547.63 + 196 = 1743.63 ft

The square root of 1743.63 is approximately 42, so Bob would need a ladder at 42 feet long.

2. The Johnsons recently moved into their new home with a movie room. Their old TV cubicle fits their old 36 inch TV.
However, Mr. Johnson bought a new TV measuring 36 inches x 22 inches. Will their new TV be able to fit into the cubicle?

Explanation:

C2 = (362 + (222) = 1780 The square root of 1780 is approximately 42 inches.

Therefore, their TV will not fit with their old cubicle.

3. A suitcase measures 38 inches long and 20 inches high. What is the diagonal length of the suitcase in ft?

Explanation:

C2 = (382 + 202)

C2 = 1844 inches

C = 43 inches Convert inches to ft

(1 inch / 0.083 ft) = (1844 inches / x)

X = 1844 x 0.083

X = 153 ft

4. The soccer field of Inter Milan is a rectangle 95 meters wide and 125 meters long. As an exercise on the players'
precision skills, they are asked to kick the ball from one corner to the other. What is this distance in ft?

Explanation:

C2 = (952 + 1252)

C2 = 24650 m

C = 157 m Convert m to ft

(1 ft / 0.3048 m) = (x / 157 m)

X = 157 / 0.3048

X = 515.1 ft