If the ratio of 3 sides of a triangle XYZ is x : y : z = 4 : 8 : 5, can we find the angles of triangle XYZ? If yes, what is the largest angle?

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I google for you,

https://www.mathsisfun.com/algebra/trig-solving-sss-triangles.html

Seems like I have to re=learn my o level to prepare for my son secondary school.

These formulas bring back the old school day memories …..

You’re helpful ! guys.

Thank you, Ender. Very useful link.

Lol. We found the same article 🙂

Here’s a good article that explains how to use the law of cosines to find angles in a triangle when all 3 sides are given.

The largest angle C will be the angle formed from the 2 sides a=4u and b=5u. The longest side c=8u will form the base of the triangle.

Hence, cos (C) = (a^{2} + b^{2} – c^{2}) / 2ab = (4^{2} + 5^{2} – 8^{2}) / 2(4)(5) = -0.575

Hence C = cos^{-1}(-0.575) = **125.1 ^{o}**

#Corrected 9 Oct.

Here’s a good article that explains how to use the law of cosines to find angles in a triangle when all 3 sides are given.

The largest angle C will be the angle formed from the 2 sides a=4u and b=5u. The longest side c=8u will form the base of the triangle.

Hence, cos (C) = (a^{2} + b^{2} – c^{2}) / 2ab = (4^{2} + 5^{2} – 8^{2}) / 2(4)(5) = -0.575

Hence C = cos^{-1}(-0.575) = **125.1 ^{o}**

#Corrected 9 Oct.

Thanks, Chief. You have been a great help. But I believe you made a computational error. Should be -0.575

🙂

You are right! Next time I need to use a proper calculator instead of the one in Windows.