### 3 Answers

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- PhilipLv 61 month ago
By law of cosines a^2 = b^2 + c^2 - 2bc*cos A.

b = 2, c = 5rt3, A = 30 deg. rt = ''square root of''.;

So a^2 = 2^2 + (5rt3)^3 -2*2*5rt3*cos30deg;

= 79 -20rt3(1/2)rt3)= 79-30 = 49. Then a = 7.;

Option D. gives correct answer.

- PuzzlingLv 71 month ago
You have two sides and an included angle (30°), so use the Law of Cosines. I'm using the version with a² on the left hand side because you are looking for a.

a² = b² + c² - 2bc cos A

A = 30°

b = 2

c = 5√3

Plug in, solve for a², then take the square root.

a² = 2² + (5√3)² - 2(2)(5√3) cos(30°)

a² = 4 + (25*3) - 20√3 * √3/2

a² = 4 + 75 - 20 * 3/2

a² = 79 - 30

a² = 49

a = √49

a = 7

Answer:

D. 7

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