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).

Correct answer:

α =  21.7868 °
β =  38.2132 °
γ =  120 °

Step-by-step explanation:

a=3 b=5 c=7  a2 = b2+c2 − 2⋅ bc cos α A=arccos((b2+c2−a2)/(2⋅ b⋅ c))=arccos((52+72−32)/(2⋅ 5⋅ 7))≐0.3803 rad  α=A→  °=A⋅ π180​   °=0.3803⋅ π180​   °=21.787  °=21.7868∘=21°47′12"
b2 = a2+c2 − 2 ac cos β B=arccos((a2+c2−b2)/(2⋅ a⋅ c))=arccos((32+72−52)/(2⋅ 3⋅ 7))≐0.6669 rad β=B→  °=B⋅ π180​   °=0.6669⋅ π180​   °=38.213  °=38.2132∘=38°12′48"
γ=180−α−β=180−21.7868−38.2132=120∘

Try calculation via our triangle calculator.


Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
The Pythagorean theorem is the base for the right triangle calculator.
Do you want to convert time units like minutes to seconds?
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: