Practice 7A 2
1. The area of a square is 20 m . What is the perimeter of the square to the nearest tenth? 2. What is the length of a diagonal of a square with sides of length 4? 3. What is the length of a side of a square with a diagonal of length 4? 4. What is the value of x? 6. What is the height of the trapezoid? 7. What is the height of the trapezoid? 5. What is the value of y? 8. What is the area of the parallelogram? 9. A farmer’s land has the shape and dimensions shown in the coordinate grid. Each unit on the grid represents 1 km. What is the perimeter of the farmer’s land to the nearest tenth of a kilometer? 10. A square has a diagonal with a length of 20. Which of the following are true? I. One side of the square is !10 2 . II. The square is also a rectangle. 2
III. The area of the square is 400 units . Practice 7B 1. The longer leg of a 30°-­‐60°-­‐90° triangle is 6. What is the length of the hypotenuse? 2. The shorter leg of a 30°-­‐60°-­‐90° triangle is 6. What is the length of the longer leg? 3. The hypotenuse of a 30°-­‐60°-­‐90° triangle is 30. What is the length of one of its legs? 4. The longer leg of a 30°-­‐60°-­‐90° triangle is 30. What is the length of the shorter leg? 5. What are the values of x and y? 6. What is the area of the triangle? 7. What is the value of x? Round your answer to the nearest 8. What is the value of y? tenth. 9. What is the value of x? 10. What is the value of x? Practice 7C 1. Choose the correct expression for tan H. GK
A. ! KH
GH
B. ! KH
GK
C. GH
!
KH
D. !KG
2. In ΔSTU, what is the sine ratio of ∠T? 3. Which of the following equations could be used to solve for x? x
A. sin38° =
24
!
x
B. cos38° =
24
!
24
C. sin38° =
x
!
24
D. cos38° =
x
!
4. An 18-­‐ft ladder makes an angle of 55° with the ground. What is the distance, in feet, from the bottom of the ladder to the wall? Round to the nearest hundredth. 5. What is the value of x to the nearest hundredth? Practice 7D 1. At a certain time, a vertical pole 10 ft tall casts a 14-­‐ft shadow. What is the angle of elevation of the sun to the nearest degree? 2. Which expression gives the length of segment RS? A. 10 sin 18° B. 10 cos 72° C. 10 sin 72° D. 10 tan 72° 3. In the figure, which angle has the greatest sine ratio? A. ∠1 B. ∠2 C. ∠3 D. The three angles have the same sine. 4. What is the value of x to the nearest foot? 5. What is the value of x to the nearest whole number? Practice 7E 1. Alison lets out 50 ft of twine on her kite. The angle of elevation is 55°. To the nearest foot, how high above Alison’s hands is the kite? 2. A ship’s anchor rests on the sea floor 125 ft below the surface. The angle of elevation from the anchor to the ship is 38°. How long is the anchor chain to the nearest foot? 3. A surveyor measures the top of a building 50 ft away from him. His angle-­‐measuring device is 4 ft above the ground. The angle of elevation to the top of the building is 63°. How tall is the building to the nearest foot? 4. A 120-­‐ft tall building casts a shadow of 90 ft long. To the nearest whole degree, what is the angle of elevation of the sun? 5. A person standing 30 ft from a flagpole can see the top of the pole at a 35° angle of elevation. The person’s eye level is 5 ft from the ground. To the nearest foot, what is the height of the flagpole? Practice 7F 1. What is the value of x? 2. What is the length of the hypotenuse of the triangle to the nearest tenth? 4. What is the value of x? 5. What is the value of y? 6. Sam’s Sailboats is making a sail in the shape of a right triangle. The longest side of the sail is 65 ft and the sail must be 55 ft high. To the nearest square foot, how much cloth is needed to make the sail? 7. The length of a diagonal of a square is 14 cm. What is the area of the square? 3. What is the perimeter of △ABC to the nearest tenth? 8. What is the value of x? 9. What is the value of y? 10. An equilateral triangle has an area of 400 square inches. What is the length of each side? 11. A 107-­‐ft tall building casts a shadow of 90 ft. To the nearest whole degree, what is the angle of elevation to the sun? 12. The angle of depression of a submarine from another Navy ship is 28°. The submarine is 791 ft from the ship. About how deep is the submarine? 13. A kite on a 100-­‐ft string has an angle of elevation of 18°. The hand holding the string is 4 ft from the ground. How high above the ground is the kite? 14. What is the ratio for sin(A)? 15. Which of the following statements is NOT true? 3
3
A. sin A = B. cos C = 5
5
!
!
4
4
C. cos A =
D. tan C =
5
3
!
!
()
()
()
()