Name Algebra2 & Stats
1. A landscape designer is designing a triangular garden with two sides that are 4 feet and 6 feet, respectively. The angle opposite the 4-foot side is 30 degrees. How many distinct triangles can the designer make using these measurements?
2. In triangle ABC, a = 20, b = 16, and m<A = 30. Triangle ABC
a. Must be a right triangle
b. Must be an acute triangle
c. Must be an obtuse triangle
d. Could be an acute or obtuse triangle
3. An isosceles triangle has base angles of 53.4 degrees and a base equal to 14.7 inches. Find, to the nearest tenth of an inch, the length of the equal sides of a triangle.
4. In triangle ABC, side a = 18, sinA = ¾, and the sinB = 2/3. Find the length of side b.
5. A parallelogram with sides of 15cm and 18cm contains a 57.6 degree angle. Find the length of the shorter diagonal of the parallelogram, to the nearest tenth of a centimeter.
6. Katie is out with her parents at the Long Island Fair when she sees a large balloon with her name on it. Her dad tells her the angle of elevation from where she is standing to the foot of the balloon is 32 degrees but Katie is in too much of a hurry to listen. She runs 120 feet toward the area where the balloon is hovering before her mom, a math teacher, catches up with her and says that the angle of elevation from where she is now to the foot of the balloon is 54 degrees. But Katie only wants to know one thing. “I want to go up there. How high up is it?” she asks. Answer Katie’s question to the nearest tenth of a foot.
7. A surveyor is mapping a triangular plot of land. He measures two of the sides and the angle formed by these two sides find that the lengths are 400 yards and 200 yards and the included angle is 50 degrees. What is the measure of the third side of the plot of land, to the nearest yard?
8. a. In triangle CTH, m<C = 17, c = 12, and h = 31. How many distinct triangles CTH are possible?
b. Find all possible measures of <T, to the nearest degree.
c. Find all possible lengths of CH, to the nearest integer.
9. a. Find the measure of the smallest angle in a triangle given side lengths of 5, 9 and 11. Round your answer to the nearest ten-minutes.
b. Using your answer from part a, find the measure of the largest angle in the triangle, to the nearest ten minutes.
10. Points A & B are on one side of a river, 100' apart, with C on the opposite side. The angles A and B measure 70º and 60º respectively. What is the distance from point A to point C, to nearest foot?
11. In a rhombus whose side measures 22 and the smaller angle is 55º, find the length of the larger diagonal, to the nearest tenth.
Solve for θ, such that 0 < θ < 360. For all of these we will just to the nearest degree so it isn’t a problem for people who do not have a graphing calculator.
12. 7 tan2θ + 3 tanθ – 9 = 0
13. 6sin2θ – 5 = 0
14. Solve the system y = 9sin2θ and y = 2cosθ + 3
15. 5cosθ + 8sin2θ = 0
16. cos2θ + 3cosθ -1 = 0
17. In the accompanying diagram of a streetlight, the light is attached to a pole at R and supported by a brace, , RQ = 10 feet, RP = 6 feet, PRQ is an obtuse angle, and mPQR = 30. Find the length of the brace, , to the nearest foot.
18. In triangle ABC, a = 19, c = 10, and m<A = 112. Which statement can be used to find the value of(1) sin C = 10 (2) sin C = 10 sin22 (3) sin C = 19sin68 (4) sin C = 10sin 68
19 19 10 19
19. Two equal forces act on a body at an angle of 80°. If the resultant force is 100 newtons, find the value of one of the two equal forces, to the nearest hundredth of a newton.
20. Two forces act on a body forming a resultant force of 46 pounds. If the angle between the resultant and the smaller force of 19.8 pounds is 54.9 degrees, what is the magnitude of the larger force, to the nearest tenth of a pound? What is the measure of the angle, to the nearest tenth, between the larger force and the resultant force?
21. Katie is out with her parents at the Long Island Fair when she sees a large balloon with her name on it. Her dad tells her the angle of elevation from where she is standing to the foot of the balloon is 32 degrees but Katie is in too much of a hurry to listen. She runs 120 feet toward the area where the balloon is hovering before her mom, a math teacher, catches up with her and says that the angle of elevation from where she is now to the foot of the balloon is 54 degrees. But Katie only wants to know one thing. “I want to go up there. How high up is it?” she asks. Answer Katie’s question to the nearest tenth of a foot.
22. Off of Route 787 in Albany, New York there is a building with a spinning U-Haul on the roof. The U-Haul has been there for years and in used as an advertisement for the company. The height of the U-Haul is 14.3 feet. From where you are standing on the ground, approaching the building, the angle of elevations to the top of the truck and to the bottom of the truck are 43 degrees and 40 degrees, respectively. How tall is the building, to the nearest foot?
23. In triangle ABC, a = 20, b = 16, and m<A = 66. Triangle ABC
a. must be a right triangle
b. must be an acute triangle
c. must be an obtuse triangle
d. could be an acute or obtuse triangle
24. The area of a triangle DEF is 65.4 square units. If DE = 11 and FE = 18, what is the measure of the acute angle E to the nearest hundredth?
An airplane traveling at a level altitude of 2050 feet sights the top of a 50-foot tower at an angle of depression of 28° from point A. After continuing in level flight to point B, the angle of depression to the same tower is 34°.
To the nearest foot, the distance traveled from point A to point B is
26. A ship captain at sea uses a sextant to sight an angle of elevation of 37° to the top of a lighthouse. After the ship travels 250 feet directly toward the lighthouse, another sighting is made, and the new angle of elevation is 50°. The ship's charts show that there are dangerous rocks 100 feet from the base of the lighthouse. Find, to the nearest foot, how close to the rocks the ship is at the time of the second sighting.
27. Carmen and Jamal are standing 5,280 feet apart on a straight, horizontal road. They observe a hot-air balloon between them directly above the road. The angle of elevation from Carmen is 60° and from Jamal is 75°. Find the height of the balloon to the nearest foot.
12. The accompanying diagram shows the approximate linear distances traveled by a sailboat during a race. The sailboat started at point S, traveled to points E and A, respectively, and ended at point S.
Based on the measures shown in the diagram, which equation can be used to find x, the distance from point A to point S?
1.
2.
3.
4.
13. As shown in the accompanying diagram, two tracking stations, A and B, are on an east-west line 110 miles apart. A forest fire is located at F, on a bearing 42° northeast of station A and 15° northeast of station B. How far, to the nearest mile, is the fire from station A?
28.