For this, you have to understand the ratios of a 30,60,90 triangle. The ratio(in order) is x, x(sqrt 3), 2x (following the 30,60,90 pattern y'know). Well, we know the length of the hypotenuse, 4.2, so let's use ratios to figure the other sides out. The ratio of AC is x and the ratio of AB is 2x, so 2x/2=x=2.1. One side down. BC has a ratio of x(sqrt 3). We already know x so we can substitute it in. We get 2.1(sqrt 3). To calculate the area, use the formula 1/2(bh). Inputting the values in, we get 1/2(2.1*(2.1(sqrt 3)). This can be calculated to around 3.82. To calculate the perimeter, take the sum of the sides. By adding the sides together, we get about 9.98. Hope you can now understand how to do these kinds of questions.
The law of cosines is used for calculating one side of the triangle if the angle opposite to that side is given as well as the other sides. For this problem, we are given angle B. Therefore, the correct answer among the choices given is option 1 where a is equal to 5 and c is equal to 3.
