# Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle?

« Correct result

#### Solution:

$c^2 = a^2 + b^2 - 2ab \cos \gamma \ \\ \ \\ \gamma = 90^\circ \Rightarrow \cos 90^\circ =0 \ \\ c^2 = a^2 + b^2 - 2ab \cos 90^\circ \ \\ c^2 = a^2 + b^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Cosine rule uses trigonometric SAS triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
2. Centre of mass
The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
3. Angles by cosine law
Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
5. RT triangle and height
Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
6. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
7. Triangle ABC
In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
8. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
9. Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
10. Euclidean distance
Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
11. Seats
Seats in the sport hall are organized so that each subsequent row has five more seats. First has 10 seats. How many seats are: a) in the eighth row b) in the eighteenth row
12. Six terms
Find the first six terms of the sequence a1 = -3, an = 2 * an-1
13. Inner angles
The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
14. Calculation of CN
Calculate: ?
15. Sequence 3
Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
16. Greatest angle
Calculate the greatest triangle angle with sides 197, 208, 299.
17. Rhomboid
The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?