Section G.3 – Practice Problems

Round your answers to two decimal places unless otherwise noted.

1. Find the length of the hypotenuse of the triangle pictured below. Write your answer in exact form and in approximate form, rounded to the nearest thousandth.

2. Find the length of the hypotenuse of the triangle pictured below. Write your answer in exact form and in approximate form, rounded to the nearest thousandth.

3. Find the length of the leg a. Write your answer in exact form and in approximate form, rounded to the nearest thousandth.

4. Find the length of the leg b. Write your answer in exact form and in approximate form, rounded to the nearest thousandth.

5. Laptop computers are measured according to the diagonals of their screens. An 18-inch laptop has a screen that is 9 inches tall. Round all answers to the nearest hundredth.

a. How wide is the screen?
b. How wide is the screen?

6. A cable is installed around two edges of the rectangular field that is 860 feet long and 340 feet wide, as shown below. Suppose the cable costs $2100 per foot to install. Round all answers to the nearest hundredth.

a. How much did it cost to run the cable along the two edges of the field?

b. How much would it have cost to run the cable along the diagonal?

c. How much money would have been saved if the cable were installed along the diagonal of the field instead of around the edges of the field?

7. Two trains leave the station at the same time. Train A travels south at a rate of 25 miles per hour south and train B travels east at a rate of 20 miles per hour. How far apart are the trains 6 hours after they leave the station? Round your answer to the nearest tenth.

8. You need to paint the trim of a window on the exterior of a house. The window is 12 feet above the ground and your ladder is 16 feet long. How far is the base of the ladder from the side of the house? Round your answer to the nearest tenth.

9. A farmer is fencing off part of his property where he would like his cattle to graze. The known lengths of the sides of the area to be fenced are shown in the diagram below. Round all answers to the nearest hundredth.

a. Find the length of the fencing for the remaining side of the area being fenced off.

b. Find the area in square feet of the fenced off region.

10. The given triangles are similar. Find x.

11. The given triangles are similar. Find x.

12. You are building a scale model of your uncle’s fishing boat. The boat is 62 ft long and 23 ft wide. The model will be 14 inches long. How wide should it be?

13. A scale model of the Titanic is 107.5 inches long and 11.25 inches wide. The Titanic itself was 882.75 feet long. How wide was it?

14. The given triangles are similar. Find j and k.

15. The given triangles are similar. Find x.

16. Find the height of the tree.

17. A statue honoring Kobe Bryant can be found in Los Angeles near the Staples Center. Use the information below to determine the unknown height of the statue.

18. A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad’s shadow?

19. A 40-foot flagpole casts a 25-foot shadow. Find the shadow cast by a nearby building 200 feet tall.

20. A man 6 feet tall casts a shadow that is 11 feet long. A building casts a shadow of 139 feet long. What is the height of the building?

21. Two extension ladders are leaning at the same angle against a vertical wall. The 3-m ladder reaches 2.4 m up the wall. How much farther up the wall does the 8-m ladder reach?