REVIEW 5

Similarity, Right Triangle Trigonometry, and Trigonometry in Other Triangles

The questions in this review section brings together the concepts from Chapters 9, 10, and 11. Use this opportunity to test your understanding of similar triangles and the application of those ideas to solve for missing measurements by using trigonometry in triangles, whether right, acute, or obtuse. Answer all the questions, and try to express your thinking as clearly as you can.

1.   Write a correct similarity statement for the triangles below.

2.   If there is sufficient information to conclude that the triangles below are similar, write an extended proportion relating the sides. If there is not enough information, tell what else is needed.

3.   In the figure below, . Prove .

4.   In the figure below, ∠X ≅ ∠ZWY. Prove ΔWYZ ~ ΔXWZ.

5.   In ΔABC, ∠DEA ≅ ∠EAC. Prove .

6.   In ΔPQR, and ∠PRS ≅ ∠Q. Prove .

7.   In ΔJKL, JK = 17 cm and JL = 25 cm. If ΔJKL ~ ΔDEF and DF = 30 cm, find DE.

8.   ΔABC ~ ΔXYZ. If AB = x – 3 cm, BC = 3 cm, AC = x – 1 cm, YZ = 21 cm, and XY = 2x + 4 cm, find the perimeter of ΔXYZ.

9.   At a certain time of day, a 10-foot tree that stands perpendicular to the ground casts a shadow on the ground. The tip of the shadow is 18 feet from the base of the tree. How far from the base of the tree should a 6-foot tall man stand so that the tip of his shadow falls at the tip of the shadow of the tree?

10.   Jason and Brianna are constructing a scale model of a park in their neighborhood. The park is triangular and their model is similar to the original, but reduced in size. If one side of the park measures 153 meters, and is represented on the model by an edge 38.25 cm long, how long should Jason and Brianna make the edge representing the 119-meter side?

11.   Use the triangle below to express each of the following.

a)  sin ∠R

b)  tan ∠T

c)  cos∠R

d)  cos∠T

e)  csc∠R

12.   In right triangle ΔABC, m∠B = 90°, m∠C = 34°, and AB = 12 cm. Find the length of the hypotenuse.

13.   Find the measure of the smallest acute angle in a 3-4-5 right triangle.

Use the following information for questions 14 through 16. In right triangle ΔRST with hypotenuse , sin∠R = 0.2.

14.   Find csc∠R.

15.   Find sec∠T.

16.   Find cos∠R.

17.   In ΔJKL, m∠J = 63°, m∠L = 51°, and JL = 20 cm. Find the length of .

18.   In ΔXYZ, XY = 45 cm, YZ = 52 cm, and XZ = 55 cm. Find the measure of ∠X.

19.   Find the area of ΔABC if AB = 18 inches, BC = 24 inches, and m∠B = 65°.

20.   The area of ΔXYZ is A = 775.9 square meters. If XY = 54 m and YZ = 68 m, find the measure of ∠Y.