In the triangle below, determine the value of a.

51sin(47) because 51 is the hypotenuse and a is the opposite so we use sine because sine=opp/hypotenuse therefore sin(47)=a/51 then rearrange the formula to make a the subject the final answer is 37.3 to the nearest 3 significant figures

To be able to solve the problem above, we use trigonometric functions and their definitions. From the given, it would be useful to use the sine function which is equal to the ratio of the opposite length and the hypotenuse. We calculate as follows:

sin theta = opposite / hypotenuse
sin 47 = a / 51
a = 37.30