Please scroll down to get to the study materials.
The word "Trigonometry" is derived from the Greek word "Tri-Gonia-Metron" 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.
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 right-angled 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 = \(\sqrt{h^{2}- p^{2}}\)
Solution:
Here,
\(\angle\)ABC = \(\theta\), angle of reference.
\(\angle\)ABC = 90°
Hence,
AC = h, AB = p and BC = b
Solution:
Here,
\(\angle\)QPR = α, angle of reference.
\(\angle\)PQR = 90°
Hence,
RP = h, RQ = p and PQ = b
Solution:
Here,
\(\angle\)EFG = β, angle of reference.
\(\angle\)GEF 90°
Hence,
FG = h, EG = p and EF = b.
Solution:
Here,
\(\angle\)ABC = 90°
Hence,
or, \(\theta\) + 35° = 90°
or, \(\theta\) = 90°− 35°
∴ \(\theta\) = 55°
Solution:
\(\angle\)XYZ = 90°
Here,
or, β + 56° = 90°
or, β = 90°− 56°
∴ β = 34°
Solution:
\(\angle\)QPR = 90°
Here,
or, α + 28 = 90°
or, α = 90°− 28°
∴ α = 52°
Solution,
Here,
AB = P = 3cm
BC = b = 4cm
AC = h = ?
From the right angled ΔABC we have,
or, h = \(\sqrt{p^2+b^2}\)
or, h = \(\sqrt{3^2+4^2}\)
or, h = \(\sqrt{9+16}\)
or, h = \(\sqrt{25}\)
∴ h = 5cm
Solution:
Here,
PQ = h = 13cm
RQ = p = 12cm
PR = b = ?
From right angled ΔPQR we have,
or, b = \(\sqrt{h^2−p^2}\)
or, b = \(\sqrt{13^2−12^2}\)
or, b = \(\sqrt{169−12}\)
or, b = \(\sqrt{25}\)
∴ b = 5cm
Solution:
Here,
YZ = h = 10cm
XY = b = 6cm
XZ = p = ?
From right angled ΔXYZ we have,
or, p = \(\sqrt{h^2−b^2}\)
or, p = \(\sqrt{10^2−6^2}\)
or, p = \(\sqrt{100−36}\)
or, p = \(\sqrt{64}\)
∴ p = 8cm
Solution:
The three sides of a triangle are 5cm, 12cm and 13cm
Here,
or, 13^{2} = 5^{2} + 12^{2}
or, 169 = 25 + 144
∴ 169 = 169
i.e. h^{2} = p^{2}+ b^{2}
Hence, the triangle is right angle triangle.
Use the Pythagorean theorem, with a = 12 and b = 5.
or, c^{2}= a^{2}+ b^{2}[Pythagorean theorem]
or, c^{2}= 12^{2}+ 5^{2} [Putting value of a & b]
or, c^{2}= 144 + 25
or, c^{2}= 169
or, \(\sqrt{c^2}\) = \(\sqrt{169}\) [Squaring on both sides]
\(\therefore\) c =13
Hence, The length of the hypotenuse is 13 metres.
Solution:
Use the Pythagorean theorem, with a = 3 and b = 4.
or, c^{2}= a^{2}+ b^{2}[Pythagorean theorem]
or, c^{2}= 3^{2}+ 4^{2}[Putting value of a & b]
or, c^{2}= 9 + 16
or, c^{2}= 25
or, \(\sqrt{c^2}\) = \(\sqrt{25}\) [Squaring on both side]
\(\therefore\) c = 5
Hence, The length of the hypotenuse is 5 metres.
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?
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?
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?
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?
Ms. Reena tells you that a right triangle has a hypotenuse of 13 and a leg of 5. She asks you to find the other leg of the triangle without using paper and pencil. What is your answer?
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?
Tara runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards.What is the length of the diagonal, in yards, that Tara runs?
A house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point?
Bibek is climbing a mountain with Roshan and has just climbed a 16-metre vertical rock face. Roshan is standing 12-metre away from the bottom of the cliff, looking up at Bibek. How far away are Bibek and Roshan?
Krishna's bedroom is rectangular. The length of one wall of Krishna's bedroom is 3 metres. The length from one corner of the bedroom to the diagonally opposite corner is 5 metres. What is the length of the other wall?
Three ballet dancers are positioned on stage. Martha is straight behind Ashley and directly left of Kendrick. If Ashley and Martha are 8 metres apart, and Kendrick and Ashley are 10 metres apart, what is the distance between Martha and Kendrick?
An oak tree is 5 metres tall and a bird is standing on the ground 12 metres from the tree. If the bird flies directly to the top of the tree, how far will it fly?
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?
Lara's house is due west of Winchester and due south of Lowell. Winchester is 12 kilometres from Lara's house and 15 kilometres from Lowell. How far is Lowell from Lara's house, measured in a straight line?
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?
ASK ANY QUESTION ON Pythagoras Theorem
You must login to reply
David
1 tan×tan30÷1-tan×tan30
Mar 23, 2017
0 Replies
Successfully Posted ...
Please Wait...
1/√3 √3/2..........what is the answer plzz tell me
Mar 16, 2017
1 Replies
Successfully Posted ...
Please Wait...
The A.D.
If cosA=2p/p^2 1 then prove tanA=p^2-1/2p.
Mar 08, 2017
0 Replies
Successfully Posted ...
Please Wait...
Adarsh
What is the formula of sin?
Mar 03, 2017
1 Replies
Successfully Posted ...
Please Wait...