Answers

Exercise A:

These two triangles are similar. You only need two corresponding angles and two corresponding sides to determine this fact. Both triangles have angles of 60 and 75. This is enough to establish that the triangles are similar because if you take 60 and 75 away from 180 (the total of the angles in a triangle), then the remaining angle of K for Triangle (h) will be 45 and the corresponding angle in Triangle (g) will also be 45.

To find the length of J, you need to establish the ratio of the other corresponding sides. As the triangles are similar, you will know that the known two sides will have the same ratio – that is, 3/2 = 2.8/1.86 = 1.5.

Using this ratio, we can calculate J to be 4.8/1.5 = 3.2.

Exercise B:

This is the value of x in Triangle (j):

This is the value of x in Triangle (k):

Exercise C:

(X) To find θ, we must use the cosine rule, which, when written as a Google search, becomes arccos...