Laws

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

Law of sines
Law of cosines « Correct result
Law of tangents
Law of cotangents

Step-by-step explanation:

$$\begin{gathered} c^2=a^2+b^2-2ab\cos \gamma \\ \gamma =90^{\circ }\Rightarrow \cos 90^{\circ }=0 \\ {c}^2=a^2+b^2-2ab\cos 90^{\circ } \\ {c}^2=a^2+b^2-2ab\cdot 0 \\ {c}^2=a^2+b^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Without Euclid laws
  Right triangle ABC with right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws.
• 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).
• Triangle ABC
  Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
• Two triangles SSA
  Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
• Largest angle of the triangle
  Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
• ABCD
  AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
• Triangle and its heights
  Calculate the length of the sides of the triangle ABC, if v_a=5 cm, v_b=7 cm and side b is 5 cm shorter than side a.
• Calculate triangle
  In the triangle ABC, calculate the sizes of all heights, angles, perimeters and its area, if given a-40cm, b-57cm, c-59cm
• Triangle's centroid
  In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
• Medians of isosceles triangle
  The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What is the length of medians?
• Space vectors 3D
  The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
• Triangle
  Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM. Calculate its area and its interior angles.
• The aspect ratio
  The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
• Mast shadow
  Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
• Aircraft bearing
  Two aircraft will depart from the airport simultaneously, the first with a course of 30° and the second with a course of 86°. Both fly at 330 km/h. How far apart will they be in 45 minutes of flight?
• Triangle SAS
  Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• River
  From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river.