Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes:
2a, 3/2a, 3a

Correct result:

C =  117.28 °

Solution:

x=1 a=2 x=2 1=2 b=3/2 x=3/2 1=32=1.5 c=3 x=3 1=3  c>a>b c2=a2+b22 a b cos(C) C=180πarccos(a2+b2c22 a b)=180πarccos(22+1.52322 2 1.5)=117.28=1171647"x=1 \ \\ a=2 \cdot \ x=2 \cdot \ 1=2 \ \\ b=3/2 \cdot \ x=3/2 \cdot \ 1=\dfrac{ 3 }{ 2 }=1.5 \ \\ c=3 \cdot \ x=3 \cdot \ 1=3 \ \\ \ \\ c>a>b \ \\ c^2=a^2+b^2 - 2 \cdot \ a \cdot \ b \cdot \ \cos(C) \ \\ C=\dfrac{ 180^\circ }{ \pi } \cdot \arccos (\dfrac{ a^2 + b^2 - c^2 }{ 2 \cdot \ a \cdot \ b } )=\dfrac{ 180^\circ }{ \pi } \cdot \arccos (\dfrac{ 2^2 + 1.5^2 - 3^2 }{ 2 \cdot \ 2 \cdot \ 1.5 } )=117.28 ^\circ =117^\circ 16'47"

Try calculation via our triangle calculator.




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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Do you have a system of equations and looking for calculator system of linear equations?
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Alfa, beta, gama
    angles_in_triangle In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
  • Angles by cosine law
    357_triangle 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 from median
    triangles_1 Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
  • In a 2
    angles_7 In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
  • SSA and geometry
    ssu_veta The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
  • Viewing angle
    zorny The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
  • Medians of isosceles triangle
    iso1 The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
  • A triangle
    triangle1_1 A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
  • Triangle 42
    triangle2_4 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
  • Right triangle
    rebrik_7 Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
  • Trapezium internal angles
    lichob_2_2 A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
  • Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  • Two triangles SSA
    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
  • Gasoline canisters
    fuel_4 35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canis
  • Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
  • Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  • Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144