The second year of high school solves triangles, and the second year of high school mathematically s

It is known that a = 34 degrees, b = 56 degrees, then c = 90 degrees. sinc=1 with the sine theorem, a=sina*c sinc

b=sinb*c/sinc

You can find it by substituting the number. Calculate with a calculator.

Solution: Because tana+tanb= 3tanatanb- 3=- 3(1-tanatanb).

So (tana+tanb) (1-tanatanb)=-3, i.e. tan(a+b)=-3

So tanc = tan (180° - a-b) = -tan (a + b) 3 easy to get angle c = 60°

Then the product of the triangle is s=1 2 *ab*sinc=(3 3) 2, that is, ab*( 3 2)=3 3

AB 6 is obtained by the cosine theorem c = a +b -2abcosc and c = 7 transport shed 2

So 49 4 = a +b -ab i.e. a +b 73 4 then (a + b) = a +2ab + b =73 4 + 12 = 121 4 Jie Qi Pei De a + b = 11 2

From tana+tanb=3, tanatanb=- 3, the nuclear group can be calculated that tan(a+b) is also equal to -tanc, and then the result can be calculated according to the area of c=7 lead 2 and huaijiao abc is (3 3) 2.

Now I forgot that I feel that I use the angle of the c of the spine of tan (a+b) to bring in the area formula to use the sine to find the value of ab, and then use the cosine formula to find the square of (a+b), which should be fine. Anyway, I think this kind of question just remember the idea.,Talk about the conditions to push in the direction you're familiar with.,Finally, just connect it to get the result.。。

The height is sin20°

If the height does not change, the slope angle is changed to 10

Then the slope length is a rough excavation for leakage:

sin20/sin10°=2cos10°

Take the midpoint of the ac side as e, because ac=7, the midline on the bc side ad=, we get ae=ec=ad=7 2,de stool =1 2ab=2ad 2=ae 2+de 2-2ae*decosaed7 2) 2=2 2+(7 2) 2-2*2*(7 2)cosaed (1).

dc^2=de^2+ec^2-2de*eccosdecdc^2=2^2+(7/2)^2-2*2*(7/2)cosdec (2)

From (1) we get 2*2*(7 2)cosaed=2 2 because the angle aed + angle dec=180

cosaed=-cosdec

2*2*(7 2)cosdec=-2 2 is brought into (2), and dc 2=2 2+(7 2) 2+2 2=81 nucleus 4dc=9 2

So bc=9

cosa=(b2+c2-a2) (2bc)=(c2+3) 4c, the denominator is less than a 4c, sort out the fraction, get the post-formula, the post-denominator is coarsely sorted, use c+3 c >=2 * root number 3, and then the whole eggplant friendli, you get the root number 3 2.