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"Is the ship in danger of running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 4
Knowledge explanation
1. Review the questions and draw pictures.
(Reference data: sin55º=0.819, cos55º=0.574, tan55º=1.428, Sin25º=0.423, cos25º=0.906, tan25º=0.466)
There is a small island A in the vast sea. There are reefs within 10 nautical miles of the island. Today, a cargo ship sails from east to west. It starts at B, 55° south of island A, and travels 20 nautical miles west to reach the island. After C at 25° east of south, the cargo ship continued to sail westward.
Do you think the cargo ship will be in danger of running aground on the rocks as it continues sailing west?
2. Review the drawings to determine what is known and what is unknown.
3. Assume appropriate unknowns and formulate equations
4. Solve equations and conclude.
As shown in the picture, Xiao Ming wants to measure the height of tower CD. He looks up at the top of the tower at point A and measures the elevation angle to be 30°. He then moves 50m toward the tower to point B and measures the elevation angle to be 60°. Then how high is the tower? ?(Xiao Ming’s height is ignored, and the result is accurate to 1m).
Can you complete this task now?
To solve this problem, we still need to mathematicalize it.
As shown in the figure, the cross-section of the reservoir dam is trapezoid ABCD, the top of the dam is AD=6m, the slope length is CD=8m. The bottom of the slope is BC=30m, and ∠ADC=135°.
(1) Find the size of ∠ABC (accurate to 1°);
(2) If the dam is 100m long, how much earth and stone is needed to build the dam (the result is accurate to 0.01m3).
Practice in class
1. (2011·Zhuzhou High School Entrance Examination) As shown in the picture, Kong Ming, carrying a bucket of water, started from the foot of the mountain A and walked up the hillside at an angle of 30° to the ground, delivering water to Grandma Wang’s house on the mountain, which was short of water due to drought this spring. (at B), AB=80 meters, then the height BC that Kongming ascends from A to B is _____ meters.
[Analysis] According to the question, ∠ACB=90°. So sin∠A=sin30°=BC/AB=BC/80, so BC=40 (meters).
Answer: 40
2. (2010·Hengyang High School Entrance Examination) In order to bid for the 2010 Winter Olympics, the traffic conditions in Harbin must be changed. In the widening project of Dazhi Street, a tree AB must be cut down, and a circle with B as the center and a radius must be cut down on the ground. A circular danger zone with the same length as AB. Now a worker is standing at D 3 meters away from point B. From point C, the elevation angle of point A at the top of the tree is 60°, and the depression angle at point B at the bottom of the tree is 30°. °.
Question: Is the protective object 8 meters away from point B within the danger zone?
[Rule method] Draw geometric figures according to the meaning of the question, construct a right triangle, and flexibly use the definition of trigonometric functions combined with the relevant knowledge of the Pythagorean theorem are the keys to solving the problem.
General steps for solving word problems of practical significance:
1. Review the questions and draw pictures.
2. Review the drawings to determine what is known and what is unknown.
3. Assume appropriate unknowns and form an equation.
4. Solve equations and conclude.
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For more information about the PPT courseware "The relationship between the sides and angles of a right-angled triangle. Is there a danger of a ship running aground on the rocks?", please click the ppt tag of "The relationship between the sides and angles of a right-angled triangle: Is there a danger of a ship running aground on the rocks?"
"Is there a danger of the ship running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 3:
"Is the ship in danger of running aground on the rocks?" Relationship between the sides of a right triangle PPT courseware 3 Is the ship in danger of running aground on the rocks? There is a small island A in the sea. There are reefs within 10 nautical miles of the island. Today, a cargo ship sailed from west to east. It started at B, 60 degrees west of south of island A, and then traveled 20 nautical miles east...
"Is there a danger of the ship running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 2:
"Is there a danger of the ship running aground?" The relationship between the sides and angles of a right triangle PPT courseware 2 Review and think about the relationship between the sides and angles of a right triangle The relationship between the three sides of a right triangle: Pythagorean theorem a2+b2=c2. The relationship between the two acute angles of a right triangle: two Acute angles are complementary to each other A+B=90. Three right angles..
"Is the ship in danger of running aground on the rocks?" PPT courseware on the relationship between the sides and angles of a right triangle:
"Is there a danger of the ship running aground on the rocks?" The relationship between the sides of a right triangle PPT courseware Think about it as shown in the figure. There is a small island A in the sea. There are reefs within 10 nautical miles around the island. Today, a cargo ship sails from west to east and starts to go south and west of island A. 55 B, drive east for 20 nautical miles and then reach the south of the island..