Part A: First, list multiples for each number. The multiples of 5 are: 5, 10, 15, 20, 25 30, 35, 40, 45, 50, 55, 60, etc. The multiples of 12 are: 12, 24, 36,48, 60, etc. The least common multiple is the first common multiple between the two, in this case being 60. The LCM of 5 and 12 is 60.
Part B: SImilar to above, list all factors for each number. 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. 81: 1, 3, 9, 27, and 81. The greatest common factor is the highest common number, 9 in this case. The GCF of 72 and 81 is 9.
Part C: To rewrite, we need to take out the 9 by dividing. 72/9 is 8. 81/9 is 9. Therefore, we would get 9(8+9), to equal 153. Your answer here is 9( 8 + 9 ). Hope this helped!
If HG and GF are both 3, then the whole length of the base is 6. The tan ratio is the side opposite the reference angle (length 4) over the side adjacent to the angle (length 6), which for us looks like this: Now use the inverse tan button (2nd-->tan) to get As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this: Solving for y and using the inverse sin gives you that y = 53.12 If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.