"Application of Solving Right Triangles" PPT Courseware 2

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"Application of Solving Right Triangles" PPT Courseware 2

1. Among the angles formed by the line of sight and the horizontal line, the line of sight on the ______ side of the horizontal line is called the elevation angle, and the line of sight on the ______ side of the horizontal line is called the depression angle.

2. As shown in the figure, the ratio hl of the vertical height h of the slope to ___________ is called the slope (or ________) of the slope, and the _______ between the slope and the horizontal plane is called the slope angle, that is, tan α = ______. Obviously, the more the slope angle The larger the slope, the steeper the slope.

1. (4 points) (2013·Shanxi) As shown in the figure, to build a highway in a certain place, a tunnel needs to be built from point B to point C (B and C are on the same horizontal plane). In order to measure the distance between places B and C, An engineer takes a hot air balloon from point C, rises vertically 100 m to point A, and observes point B at point A.

The angle of depression of the ground is 30°, then the distance between places B and C is ()

A． 1003mB． 502 m

C. 503 m D.10033 m

2. (4 points) As shown in the figure, student Zhang Hua measured the elevation angle of point A at the top of the flagpole at point C of a building in the school to be 30°, and the depression angle at point B at the bottom of the flagpole was 45°. If point B at the bottom of the flagpole reaches the point of the building The horizontal distance BE = 9 meters, the height of the flagpole step is 1 meter, then the height of the flagpole vertex A from the ground is ________ meters (the result retains the root sign).

16. (8 points) Xiao Liu observed the working process of the crane in extracurricular activities and drew the plane figure as shown in the figure. It is known that the height of the fulcrum O of the crane's boom from the ground OO' = 2 meters. When the boom When the top is lifted from point A to point A′ (the length of the boom remains unchanged), the weight at B on the ground (the size is ignored) is lifted to point B′, and the tight sling A′B′=AB.AB The vertical ground O'B is at point B, A'B' is perpendicular to the ground O'B at point C, the length of the boom OA'=OA=10 meters, and cos A=35, sin A'=12.

(1) Find the distance BC that the weight moves in the horizontal direction;

(2) Find the distance B′C that the weight moves in the vertical direction. (The result retains the square root)

16.(1) Let OD⊥AB be at point D, and intersect A′C at point E,

Then EC=DB=OO′=2, ED=BC,

AD＝OA·cos A＝6，∴OD＝8，

OE＝OA′·sin A′＝5，∴BC＝3(meters)

(2)A′E＝A′O2－OE2＝53,

∴B′C＝A′C－AB＝A′E＋CE－AB＝

A′E＋CE－(AD＋BD)＝53－6(meter)

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"Applications of Solving Right Triangles" PPT courseware:

"Solution to Right Triangle" PPT courseware 2 Review the past and learn new things 1. The relationship between the sides and angles of a right triangle: (1) The relationship between angles: A+B = 90; (2) The relationship between sides: a2+b2=c2; (3) Angle and side The relationship between: sinA=a/c, cosA=b/c, tanA..

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Update Time: 2024-06-07

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