Answer:
The measure of the largest angle is 120°
Step-by-step explanation:
<em>Lets explain how to find the measure of an angle from the length of the </em>
<em>sides of the triangle</em>
- We can do that by using the cosine rule
- If the three angles of the triangle are A , B , C, then the side opposite
to angle A is BC , the side opposite to angle B is AC and the side
opposite to angle C is AB, So to find measure of angle A use the rule
![cos(A)=\frac{(AB)^{2}+(AC)^{2}-(BC)^{2}}{2(AB)(AC)}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B%28AB%29%5E%7B2%7D%2B%28AC%29%5E%7B2%7D-%28BC%29%5E%7B2%7D%7D%7B2%28AB%29%28AC%29%7D)
<em>Lets solve the problem</em>
- Assume that the triangle is ABC where AB = 14 cm , BC = 10 cm and
AC = 6 cm
- We need to find the measure of the largest angle
- The largest angle is opposite to the longest side
∵ The longest side is AB
∴ The largest angle is C
By using the rule above
∴ ![cos(C)=\frac{(AC)^{2}+(BC)^{2}-(AB)^{2}}{2(AC)(BC)}](https://tex.z-dn.net/?f=cos%28C%29%3D%5Cfrac%7B%28AC%29%5E%7B2%7D%2B%28BC%29%5E%7B2%7D-%28AB%29%5E%7B2%7D%7D%7B2%28AC%29%28BC%29%7D)
∵ AB = 14 cm , BC = 10 cm , AC = 6 cm
∴ ![cos(C)=\frac{(6)^{2}+(10)^{2}-(14)^{2}}{2(6)(10)}](https://tex.z-dn.net/?f=cos%28C%29%3D%5Cfrac%7B%286%29%5E%7B2%7D%2B%2810%29%5E%7B2%7D-%2814%29%5E%7B2%7D%7D%7B2%286%29%2810%29%7D)
∴ ![cos(C)=\frac{36+100-196}{120}](https://tex.z-dn.net/?f=cos%28C%29%3D%5Cfrac%7B36%2B100-196%7D%7B120%7D)
∴ ![cos(C)=\frac{-60}{120}=-0.5](https://tex.z-dn.net/?f=cos%28C%29%3D%5Cfrac%7B-60%7D%7B120%7D%3D-0.5)
∴ cos(C) = -0.5 ⇒ that means angle C is obtuse angle
∴ m∠C = ![cos^{-1}(-0.5)=120](https://tex.z-dn.net/?f=cos%5E%7B-1%7D%28-0.5%29%3D120)
* <em>The measure of the largest angle is 120°</em>