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).


A =  21.787 °
B =  38.213 °
C =  120 °


a=3 b=5 c=7 A1=arccos((b2+c2a2)/(2 b c))=arccos((52+7232)/(2 5 7))0.3803 A=A1 =A1 180π  =21.78679  =21.787=214712"a=3 \ \\ b=5 \ \\ c=7 \ \\ A_{1}=\arccos((b^2+c^2-a^2)/(2 \cdot \ b \cdot \ c))=\arccos((5^2+7^2-3^2)/(2 \cdot \ 5 \cdot \ 7)) \doteq 0.3803 \ \\ A=A_{1} \rightarrow \ ^\circ =A_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =21.78679 \ \ ^\circ =21.787 ^\circ =21^\circ 47'12"

Try calculation via our triangle calculator.

B1=arccos((a2+c2b2)/(2 a c))=arccos((32+7252)/(2 3 7))0.6669 B=B1 =B1 180π  =38.21321  =38.213=381248"B_{1}=\arccos((a^2+c^2-b^2)/(2 \cdot \ a \cdot \ c))=\arccos((3^2+7^2-5^2)/(2 \cdot \ 3 \cdot \ 7)) \doteq 0.6669 \ \\ B=B_{1} \rightarrow \ ^\circ =B_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =38.21321 \ \ ^\circ =38.213 ^\circ =38^\circ 12'48"
C=180AB=18021.786838.2132=120=120C=180-A-B=180-21.7868-38.2132=120=120 ^\circ

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...):

Showing 0 comments:
1st comment
Be the first to comment!

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

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  2. Angles
    triangle_1111_1 In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
  3. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  4. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  5. Triangle and its heights
    triangle_2 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.
  6. Bearing - navigation
    navigation A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
  7. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  8. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  9. 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?
  10. Triangle ABC
    squares4 Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
  11. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  12. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  13. Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  14. Reference angle
    anglemeter Find the reference angle of each angle:
  15. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  16. Trigonometry
    sinus Is true equality? ?
  17. Theorem prove
    thales_1 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?