As shown in figure 1, when we measure, the angle between the line of sight and the horizontal line is called elevation angle, and the angle below the horizontal line is called depression angle.

(2) Direction angle

Refers to the horizontal angle of less than 90 between the north or the guiding direction line and the target direction line, which is called the direction angle. As shown in Figure 2, the direction of the target direction line can generally be expressed by how many degrees ××, and the direction angles can be expressed as 60 east by north, 30 west by north, 20 east by southwest and south respectively.

Thinking method:

Construct a triangle, knowing three and seeking three (at least one side is long); (2) Application problem: analysis method, reasons for holding fruit.

Third, give an example

Example 1. In, then B=

Variable: In, B=.

Note: the big side faces the big corner.

Example 2 (Shaanxi Volume 20 10) As shown in the figure, A and B are two observation points located in the east-west direction of the sea. Now there is a distress signal from a ship at point D, 45 northeast of point A and 60 northwest of point B, and a rescue ship at point C, 60 southwest of point B, goes to rescue immediately, with a speed of 30 knots.

Exercise (Hainan Volume, Ningxia, 2009) As shown in the figure, in order to understand the seabed structure of a certain sea area, we measured three points A, B and C on a straight line within the sea level. The known water depth is measured at a, b and c, and the cosine value of ∠DEF is obtained.

Homework:

1, (20 10 Beijing Literature) (7) A class designed an octagonal class emblem (pictured).

It consists of four isosceles triangles with waist length of 1 and vertex angle of/and a square with base. The area of the octagon is

(1); (2)

(c) and: (4)

2.(2007 Ningxia Li 17) As shown in the figure, when measuring the tower height on the other side of the river, you can choose two measuring points in the same horizontal plane as the tower bottom, and now measure, and the elevation angle of the top of each point is 0, so as to calculate the tower height.

3. In order to measure the sailing speed of the model airplane on the lake, students of an interest group of the model airplane adopted the following methods: setting two observation points A and B on the shore, with AB = 80m. When the airplane model is in C, the measured values are ∠ ABC = 105 and ∠ BAC = 30. In 20 seconds, the model plane will.

Share with: