Question

Hey everyone !

A triangle has sides measuring 14 cm, 10 cm and 6 cm. The measure of the largest angle of this triangle measures:
Note: Perimeter = 30


Thank you.​

Answer 1

Hello!

A triangle has sides measuring 14 cm, 10 cm and 6 cm. The measure of the largest angle of this triangle measures:

Note: Perimeter = 30

We have the following data:

p (perimeter) = 14 + 10 + 6 = 30

a = 14 cm

b = 10 cm

c = 6 cm

α (angle) = ?

*** Note: The largest angle (α) is always opposite the larger side.

We apply the data to the Cosine Law, let's see:

`a^2 = b^2 + c^2 - 2*b*c*cos\:\alpha`

`14^2 = 10^2 + 6^2 - 2*10*6*cos\:\alpha`

`196 = 100 + 36 - 120\:cos\:\alpha`

`120\:cos\:\alpha = -196 + 100 + 36`

`120\:cos\:\alpha = -60`

`cos\:\alpha = (-6\diagup\!\!\!\!0)/(12\diagup\!\!\!\!0) (/6)/(/6)`

`cos\:\alpha = (-1)/(2)`

`\boxed{\boxed{cos\:\alpha = 120\º}}\:\:\:\:\:\:\bf\purple{\checkmark}`

Answer:

The measure of the largest angle of the triangle is 120º

_______________________

`\bf\red{I\:Hope\:this\:helps,\:greetings ...\:Dexteright02!}\:\:\ddot{\smile}`

Answer 2

The measure of the largest angle is 120°

Explanation:

Lets explain how to find the measure of an angle from the length of the

sides of the triangle

- 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)=((AB)^(2)+(AC)^(2)-(BC)^(2))/(2(AB)(AC))`

Lets solve the problem

- 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)=((AC)^(2)+(BC)^(2)-(AB)^(2))/(2(AC)(BC))`

∵ AB = 14 cm , BC = 10 cm , AC = 6 cm

∴
`cos(C)=((6)^(2)+(10)^(2)-(14)^(2))/(2(6)(10))`

∴
`cos(C)=(36+100-196)/(120)`

∴
`cos(C)=(-60)/(120)=-0.5`

∴ cos(C) = -0.5 ⇒ that means angle C is obtuse angle

∴ m∠C =
`cos^(-1)(-0.5)=120`

* The measure of the largest angle is 120°