Geometry B Sample Questions
Common Core Mathematics
3rd Quarter 2012-2013
Review key unit vocabulary.
1. At the same time of day, a man who is 76 inches tall casts a 57-inch shadow and his son casts a 24-inch shadow. What is the height of the man's son? (Figures may not be drawn to scale.)
2. Given that solve for x and y.
3. Given that solve for x and y.
4. The triangles formed by two ladders leaning against a wall are similar. How long is the shorter ladder?
5. The triangles formed by two ladders leaning against a wall are similar. How long is the shorter ladder?
6.
7. and are complementary angles as shown in right triangle ABC. Find the cosine of and the sine of . Then describe how they are related.
8. and are complementary angles as shown in right triangle RST. Write the ratios, in terms of r, s, and t, when the sine and cosine are equivalent.
9. and are complementary angles as shown in right triangle PQR. Write ratios, in terms of p, q, and r, for sin R and cos P. Then describe how they are related.
10. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a plasma television screen is 16 : 9. To the nearest tenth of an inch, what is the height of a plasma television screen with a 50-inch diagonal?
11. The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram below. The construction cost has been estimated at $120 per linear foot. Find the estimated cost for constructing the street. (1 mile = 5280 ft)
12. The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram below. The construction cost has been estimated at $80 per linear foot. Find the estimated cost for constructing the street. (1 mile = 5280 ft)
13. Circle O has center (5, 5) and radius 4. Circle P has center (–2, –4) and radius 2. Which describes how Circle O can be transformed to show that Circle P is similar to circle O?
14. Circle O has center (5, 5) and radius 4. Circle P has center (–2, –4) and radius 2. Which describes how Circle O can be transformed to show that Circle P is similar to circle O?
15. Which describes how Circle C can be transformed to show that Circle D is a similar figure?
16. Brandi wants to prove that all circles are similar, but not necessarily congruent. She draws Circle Z with center (0, 0) and radius 1. She then uses transformations to create other figures. Which drawing would not help Brandi prove that all circles are similar and why?
17. James has two circular flower beds, as shown below.
1 unit = 1 meterHow can the larger flower bed be transformed to show that the two flower beds are similar in shape?
18. Which describes how Circle C can be transformed to show that Circle D is a similar figure?
19. A slide 3.2 m long makes an angle of 35° with the ground. How high is the top of the slide above the ground?
20. A slide 2.4 m long makes an angle of 34° with the ground. How high is the top of the slide above the ground?
21. A 12-foot ladder is leaning up against the side of a house. The ladder makes an angle of with the ground. How far up the side of the house does the ladder reach?
22. Find the length of the missing side. The triangle is not drawn to scale.
23. The Leaning Tower of Pisa is 179 feet high, making a 12° angle with the vertical.
Find the value of x to the nearest foot.
24. If mÐB = 15° and a = 18, use DABC below and find c.
25. If mÐB = 36° and c = 17, use DABC below and find a.
26. If a = 24 and b = 15, use DABC below and find mÐB.
27. Find the angle of depression from the top of the lighthouse to the ship if the height of the lighthouse is 150 feet and the ship is 425 feet from the base of the lighthouse.
28. How high off the ground is a kite flying on a 40-meter string when the angle of elevation
of the kite measures 35° and the hand of the person flying it is 1.8 meters above the ground?
All other questions are from test given last year and the quality core website.
Sample problems for the quality problems can be found on the quality core website using your password.
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