Respuesta :

calculista

Answer:

The measure of angle A is [tex]101\°[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]a^{2} =b^{2}+c^{2}-2(b)(c)cos(A)[/tex]

substitute the values and solve for cos(A)

[tex]31^{2} =22^{2}+18^{2}-2(22)(18)cos(A)[/tex]

[tex]cos(A)=[22^{2}+18^{2}-31^{2}]/(2(22)(18))\\ \\cos(A)=-0.193182\\ \\A=arccos(-0.193182)=101\°[/tex]

The  measure of m∠A to the nearest degree is 101°.

Using cosine rule, we can find m∠A.

Cosine formula

  • a² = b² + c² - 2bc cos A

Therefore,

31²= 22² + 18²  - 2 × 22 × 18 cos A

961 - 484 - 324 = -792 cos A

cos A =  - 153 / 792

A = cos⁻¹ -0.19318181818

A = 101.139591749

A = 101°

Therefore, the  measure of m∠A to the nearest degree is 101°.

learn more on triangle here: https://brainly.com/question/25813512

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