Question

4) In triangle ABC, AB = AC, angle ACB = 60°.find x​

Answer 1

Answer:

Law of sines: sin C/7 = sinB/8 => multiply both sides by 8. [(Sin 60⁰)8]/7= SinB => 0.9897… = SinB. Now use inverse sin (Sin¯¹). Sin¯¹(0.9897) = 81.8⁰ There would be another possible angle (180⁰ - 81.8⁰), which equals 98.2⁰, but that is not acute, so I will eliminate that option.

60⁰ + 81.8⁰ = 141.8⁰. 180⁰ - 141.8⁰ = 38.2⁰

Law of Cosines: CB² = 8² + 7² - 2(8)(7)(cos 38.2⁰) => CB² = 64 + 49 - 88 => CB² = 25. Take the square root of both sides. CB = 5

8 + 7 + 5 = 20