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stepladder [879]
2 years ago
10

Hey everyone !

Mathematics
2 answers:
zhuklara [117]2 years ago
8 0

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)}

<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)}

∵ AB = 14 cm , BC = 10 cm , AC = 6 cm

∴ cos(C)=\frac{(6)^{2}+(10)^{2}-(14)^{2}}{2(6)(10)}

∴ cos(C)=\frac{36+100-196}{120}

∴ cos(C)=\frac{-60}{120}=-0.5

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

∴ m∠C = cos^{-1}(-0.5)=120

* <em>The measure of the largest angle is 120°</em>

Svetradugi [14.3K]2 years ago
6 0

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 = \dfrac{-6\diagup\!\!\!\!0}{12\diagup\!\!\!\!0} \frac{\div6}{\div6}

cos\:\alpha = \dfrac{-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}

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