Respuesta :
Answer:
Largest angle is 94.22°
Explanation:
The sides of the triangle are given as 6 inches, 11 inches, 13 inches.
Now, we can find the respective interior angles of the triangle using cosine rule.
Thus, for the angle opposite 6 inches, let's label it A. Thus;
6² = 11² + 13² - 2(11 × 13)cos A
36 = 121 + 169 - 286cosA
36 = 290 - 286cos A
290 - 36 = 286cosA
cosA = 254/286
A = cos^(-1)0.8881
A = 27.36°
Similarly;
11² = 6² + 13² - 2(6 × 13)cos B
121 = 36 + 169 - 156cosB
121 = 205 - 156cos B
205 - 121 = 156cosB
cosB = 84/156
B = cos^(-1)0.5385
B = 57.42°
Sum of angles in a triangle is 180°
Thus;
C = 180 - (27.36 + 58.42)
C = 94.22°
Thus,largest angle is 94.22°
The sum of the internal angle of the triangle is 180 degrees. Then the measure of the largest angle is 95.22°.
What is trigonometry?
Trigonometry deals with the relationship between the sides and angles of a triangle.
A wire is 30 inches long and is bent into a triangle with sides measuring 6 inches 11 inches 13 inches find the measure of the largest angle.
Then we know that the cosine rule is given as
[tex]\rm cos\ C = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
Let the angle of the triangle be A, B, and C.
Then the first angle A will be
[tex]\begin{aligned} cos \ A &= \dfrac{6^2+11^2-13^2}{2*6*11}\\\\cos \ A&= \dfrac{36 + 121 - 169}{132}\\\\ A &= 95.22^o \end{aligned}[/tex]
And we know that the sum of the internal angle of the triangle is 180 degrees.
∠A + ∠B + ∠C = 180°
95.22° + ∠B + ∠C = 180°
∠B + ∠C = 84.78°
More about the trigonometry link is given below.
https://brainly.com/question/22698523
