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).

Your answer:

Help us improve! If you spot a mistake, please let let us know. Thank you!

Tips for related online calculators

The Pythagorean theorem is the base for the right triangle calculator.
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:

planimetry

Pythagorean theorem
triangle
law of cosines

goniometry and trigonometry

sine
cosine
arccosine

Units of physical quantities

unit conversion
angle

Grade of the word problem

high school

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

Related math problems and questions:

Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60°, and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
Rhombus diagonals
In the rhombus ABCD, the sizes of the diagonals e = 24 cm and f = 10 cm are given. Calculate the side length of the diamond and the size of the angles, and then calculate the area of the diamond.
Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC if it is given by area S = 501.9; and two interior angles α = 15°28' and β = 45°.
Triangle angle sides
In the right triangle ABC, calculate the magnitude of the interior angles if / AB / = 13 cm; / BC / = 12 cm and / AC / = 5 cm.
Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm.
Cosine
Cosine and sine theorem: Calculate all unknown values (side lengths or angles) from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm