G.SRT.C.8: Using Trigonometry to Find a Side 3
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1 Regents Exam Questions Name: 1 The tailgate of a truck is 2 feet above the ground. The incline of a ramp used for loading the truck is 11, as shown below. 3 Find, to the nearest tenth of a foot, the height of the tree represented in the accompanying diagram. Find, to the nearest tenth of a foot, the length of the ramp. 2 A surveyor needs to determine the distance across the pond shown in the accompanying diagram. She determines that the distance from her position to point P on the south shore of the pond is 175 meters and the angle from her position to point X on the north shore is 32. Determine the distance, PX, across the pond, rounded to the nearest meter. 4 In the accompanying diagram, a ladder leaning against a building makes an angle of 58º with level ground. If the distance from the foot of the ladder to the building is 6 feet, find, to the nearest foot, how far up the building the ladder will reach. 1
2 Regents Exam Questions 5 From a point on level ground 25 feet from the base of a tower, the angle of elevation to the top of the tower is 78, as shown in the accompanying diagram. Find the height of the tower, to the nearest tenth of a foot. Name: 7 In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a building, and y represents the distance from the foot of the ladder to the base of the wall. The ladder makes a 60 angle with the ground and reaches a point on the wall 17 feet above the ground. Find the number of feet in x and y. 6 Joe is holding his kite string 3 feet above the ground, as shown in the accompanying diagram. The distance between his hand and a point directly under the kite is 95 feet. If the angle of elevation to the kite is 50, find the height, h, of his kite, to the nearest foot. 8 As shown in the accompanying diagram, a ladder is leaning against a vertical wall, making an angle of 70 with the ground and reaching a height of feet on the wall. Find, to the nearest foot, the length of the ladder. Find, to the nearest foot, the distance from the base of the ladder to the wall. 2
3 Regents Exam Questions 9 Draw and label a diagram of the path of an airplane climbing at an angle of 11 with the ground. Find, to the nearest foot, the ground distance the airplane has traveled when it has attained an altitude of 400 feet. Name: 14 A parcel of land is in the shape of an isosceles triangle. The base has a length of 673 feet and the two equal legs meet at an angle of 43. Find, to the nearest square foot, the area of the parcel of land. 10 A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66. Determine the height of the tree, to the nearest foot. 11 A person measures the angle of depression from the top of a wall to a point on the ground. The point is located on level ground 62 feet from the base of the wall and the angle of depression is 52. How high is the wall, to the nearest tenth of a foot? 12 A 10-foot ladder is to be placed against the side of a building. The base of the ladder must be placed at an angle of 72 with the level ground for a secure footing. Find, to the nearest inch, how far the base of the ladder should be from the side of the building and how far up the side of the building the ladder will reach. 13 A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50. The distance between the ship on the surface and the sunken ship on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above the ocean floor, to the nearest meter, is the ship on the surface? 3
4 ID: A Answer Section 1 ANS: REF: spring9825a 2 ANS: 109. REF: a 3 ANS: REF: a 4 ANS: 10. REF: a 5 ANS: REF: a 6 ANS: 116. REF: a 1
5 ID: A 7 ANS: x = 19.6 and y = 9.8. REF: a 8 ANS: Length of ladder = 11 and distance from the base of the ladder to the wall = 4.. REF: a 9 ANS: 2,058. REF: a 10 ANS: 45. REF: a 11 ANS: REF: a 12 ANS: 114 and 37.. REF: a 2
6 ID: A 13 ANS: 153. REF: a 14 ANS: 287, REF: b 3
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11-1 Skills Practice Areas of Parallelograms and Triangles Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 18 mm 10 mm 12 mm 4 ft 60 5.5 ft 4. 14