Trigonometry Question. Please Help?

Question

Still helping the children! Thankgoodness this is these last 5 questions posted are the last questions that I need help with to help them! If you can I would appreciate it if you looked at the other four! The stuff they have to learn today makes my eyes cross! Please put all of the work and any formula you had to do as part of your answer, I need it to understand and then further explain it to him! Thankyou for all of the help!


What is the smallest angle in a triangle with sides 3 cm, 5 cm, and 7 cm? Round your answer to the nearest tenth.


Best explained answer gets the points.

Answer 1

(Coolio Russia's answer is incorrect. He assumes that the triangle is a right triangle, but that is not the case.)

Use Law of Cosines. The smallest angle (C) sits across the smallest side (c).

c^2 = a^2 + b^2 - 2 a b cos C
3^2 = 5^2 + 7^2 - 2*5*7 cos C
2*5*7 cos C = 5^2 + 7^2 - 3^2
70 cos C = 65
cos C = 0.92857
C = inv cos 0.92857 ~ 22.8*.

Answer 2

Use cosine rule and note that smallest side is opposite the smallest angle.
3² = 5² + 7² - (2 x 5 x 7).cos A
70 cos A = 25 + 49 - 9
cos A = (25 + 49 - 9) / 70
cos A = 65 / 70
A = 21.8°

Answer 3

the longest side in a triangle is the hypotenuse. so that means 7 cm is the hypotennuse, lets say side c, 5 will be side b and 3 will be side a. the easist way to find the angles is using sine, cosine, and tangent. Sine is opposite fetha over hypotenuse. cosine is adjacent fetha over hypothenuse. Tangent is opposite fetha over adjecant fetha. the opposite, adjacent, and hypotenuse are the sides. so lets say fetha will be angle A, which is the angle opposite side A (3). use a calculator to find the answer. for angle a. plug into calculator 3 divide by 7 click equals. press the 2nd button and sine. you'll get 25.4 degrees. the angle opposite the smallest side, is the smallest angle.

Answer 4

the smallest is the smallest in sine
sine x =3/7=0.4286
x=25.4