Pythagoras Theorem
Trigonometry
The word "Trigonometry" is derived from the Greek word "TriGoniaMetron" where Tri means three, Gonia means angles and Metron mean measure. So, trigonometry is a branch of mathematics which concerned with the measurement of sides, angles and their relation to a triangle.
Pythagoras Theorem
The relationship between the three sides of a triangle is simply known as Pythagoras Theorem. The relation was given by the popular Mathematician Pythagoras which is called Pythagoras theorem.
In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
According to this theorem "In any rightangled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of squares of perpendicular and base".
By Pythagoras Theorem
Hypotenuse (h^{2}) = Perpendicular (p^{2}) + Base (b^{2})
or, h^{2}= p^{2}+ b^{2}
From this theory we can derive,
h = \(\sqrt{p^{2} + b^{2}}\)
p = \(\sqrt{h^{2}  b^{2}}\)
b = \(\sqrt{h^{2}  p^{2}}\)
Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Pythagoras Theorem = Hypotenuse (h^{2}) = Perpendicular (p^{2}) + Base (b^{2})
or, h^{2} = p^{2} + b^{2}
Where, h = \(\sqrt{p^{2}+ b^{2}}\)
p = \(\sqrt{h^{2} b^{2}}\)
b = \(\sqrt{h^{2} p^{2}}\)

A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase to the nearest tenth of a foot?
2.9
26.5
2.5
30.0

A baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?
90.0
180.0
127.3
180.7

In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch?
16
21
19
14

The older floppy diskettes measured 5 and 1/4 inches on each side. What was the diagonal length of the diskette to the nearest tenth of an inch?
6.5
7.6
5.3
7.4

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10
8
5
12

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?
9.5
13.1
8.4
9.4

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60
85
70
50

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4
4.3
5
6

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14
20
36
25

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5
6
9
4

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6
10
8
12

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20
19
13
16

An envelope measures 8 centimetres by 15 centimetres. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?
18
25
15
17

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10
52
8
9

Simran is in a hot air balloon that has just taken off and is floating above its launching point. Rahul is standing on the ground, 12 metres away from the launching point. If Simran and Rahul are 20 metres apart, how high up is Simran?
42
15
16
13

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