1. In Rt△ABC, ∠ c = 90, and the following formula may not hold ().
A . Sina = sinB B . cosa = sinB c . Sina = cosB d .∠A+∠B = 90
2. The two sides of a right triangle are 6 and 8 respectively, so the length of the third side is ().
A. 10b.2c. 10 or 2d. Not sure.
3. Given the acute angle α, Tan α = COT 37, then A is equal to ().
A.37 B.63 C.53 D.45
4. In Rt△ABC, ∠ C = 90. When ∠A and A are known, the relationship to be selected is () to find C.
A.c= B.c= C.c=a tanA D.c=a cotA
5. As shown in the figure, it is a cube box with a length of 4cm. An ant is at the midpoint m of D 1C 1, and its shortest path to the midpoint n of BB is ().
A.8 B.2 C.2 D.2+2
6. It is known that ∠A is an acute angle and sinA=, then ∠A is equal to ()
30 BC to 45 BC
7. When the acute angle α >; At 30, the value of cosα is ()
A. greater than b less than c greater than d less than.
8. Xiaoming walked down a slope with a slope angle of 30 for 2 meters, so he got off ()
a . 1m b . m . c . 2d
9. It is known that in Rt△ABC, ∠ c = 90, tanA=, BC=8, then AC is equal to ().
10d 12
10.sinα= known. Find alpha. If you use a calculator to calculate, the result is "",and finally press ().
A.AC 10N B. Shielding C. Mode D.SHIFT ""
Two. Fill in the blanks (3 points for each question, *** 18 points)
1 1. As shown in the figure, if the side length of a small square in a 3× 3 grid is 1, then the perimeter of the quadrilateral ABCD is _ _ _ _ _ _.
12. Calculate 2sin30+2coS60+3tan45 = _ _ _ _ _.
13. If sin28 = cos α, α = _ _ _ _ _.
14. It is known that in △ABC, ∠ c = 90, AB= 13, AC=5, then Tana = _ _ _ _ _.
15. If the gradient of a slope is 1:, the slope angle is _ _ _ _ _ _ _.
16. As shown in the figure, the maximum height of the glass is 8 cm. If a chopstick is inserted, the maximum length outside the glass is 4cm and the minimum length is 2cm, then the inner diameter of the glass is _ _ _ _ _ _ _ _.
Iii. Answer questions (9 points for each question, * *18 points) www.czsx.com.cn
17. Solve the problem according to the following conditions: in Rt△ABC ∠ c = 90;
(1) Given a=4 and b=8, find C.
(2) given b= 10, ∠ b = 60, find a, c.
(3) Given c=20, ∠ A = 60, find A and B. 。
18. Calculate the following questions.
( 1)sin 230+cos 245+sin 60 tan 45； (2) +tan60
(3)tan2 tan4 tan6 …tan88
Fourth, solve the following problems (6 points for 19, 7 points for each other, and 34 points for * * *) www.czsx.com.cn
19. We know the four trigonometric functions of isosceles △ABC, AB=AC= 13, BC= 10, and find the vertex angle ∠ a. 。
20. As shown in the picture, the height of a tree on the flat ground is 5 meters. Observe the shadow on the ground twice. The first time is when the sun makes an angle of 45 with the ground, and the second time is when the sun makes an angle of 30 with the ground. How many meters is the shadow observed for the second time longer than that for the first time?
2 1. As shown in the figure, the dovetail groove is isosceles trapezoid, the width AD of the outer opening is 10cm, the depth of the dovetail groove is 10cm, and AB I = 1: 1 slope. Find the width BC of the inner mouth and the cross-sectional area of the dovetail groove.
22. As shown in the picture, AB is a section of binjiang road on the north bank of the river, which is 3 kilometers long, and C is the ferry on the south bank. In order to solve the cross-strait traffic difficulties, it is planned to build a bridge at C. It is measured that A is 30 northwest of C and B is northeast of C. What is the shortest bridge connecting the two sides from C? (accurate to 0. 1)
Please design a plan and measure the height of a hill around your home. The foot of the mountain is out of reach, so you are required to write down the tools you need and the data you want to measure.
24. (Additional question 10) As shown in the figure, the school installed ground receiving equipment on the roof platform. In order to prevent lightning strike, a lightning rod was installed 3 meters away from the receiving equipment. The receiving equipment must be within the included angle of 45 at the top of the lightning rod to effectively avoid lightning strike (α≤ 45). It is known that the receiving equipment is 80 cm high, so how high should the lightning rod be installed at least?
The answer is: www.czsx.com.cn.
1.A
2.c [Pointing] An edge with a length of 8 may be a right-angled edge or a hypotenuse.
3.c[ inching] tan α = COT 37, so α+37 = 90 means α = 53.
4.a [nudge] Sina =, so c =.
5. c[ inching] Mn of the expanded graph = = 2.
6.C
Cosine value of 7.7. D[ inching] decreases with the increase of angle α >; 30，cos30 =，
So COSA: 3.
CD = CE+DE & gt； 3.8 (meters)
Therefore, the lightning rod should be installed at least 3.8 meters high.
If the depression angles of two points B and C on the ground from the top of the mountain A are 45 and 30 respectively, the connecting lines between C and D and the foot of the mountain B are * * *, and if CD= 100 m, the height of the mountain is AB.
According to the meaning of the question, BD = AB/Tan30 = AB √ 3, AB/Tan45 = AB.
∫CD = BD-BC = AB(√3- 1)= 100。
∴ab= 100/(√3- 1)= 50(√3+ 1)