In ABC, a, b, and c are opposite sides of A, B, and C, respectively, 15

Have you ever learned the Pythagorean theorem for triangles? If you learn it, it's easy to solve.

1) Because A is half of C, according to the properties of RT, the side opposite by the angle of 30 degrees is half of the hypotenuse, and there are C=90 degrees, that is, B can be directly found by the Pythagorean theorem. It is equal to 4 and the root number is 3

2) Because A is not half of C, according to the properties of RT, the side opposite by the angle of 30 degrees is half of the hypotenuse, and C is not equal to 90 degrees, that is, B is equal to 90 degrees, so B can be directly found by the Pythagorean theorem. It is equal to 2 and 7

ABC is RT

and a=4, c=8, a=30 degrees.

It is derived from the orthodox.

sin∠a/a=sin∠c/c

c=90 degrees.

According to the stock theorem.

b^2+ a^2=c^2

The solution is b = 64-16 = 4 3

2) a=30 degrees, a=6, b=8

It is derived from the orthodox.

sina/a=sinb/b

sin∠b＝3/2

i.e. b arcsin(3 2).

1) There are two scenarios.

1: c = 90 degrees, a = 4 (the right angle of 30 degrees is equal to half of the hypotenuse) is found by the Pythagorean theorem b = 4 times the root number 3

2: b=90 degrees let a=x, then b=2x, from the Pythagorean theorem to find x=8 times the 3rd root number, then b = 16 times the 3rd root number

2) Same as above.

Analysis: In RT ABC, C=90°, A, B, and C are the opposite sides of A, B, C, respectively, then: C = A +B

and a and b are the two roots of the equation x -7x + c + 7 = 0 about x, so there is a theorem by Veda

a+b=7，ab=c+7

Since c = a +b = (a + b) -2ab, so

c²=49-2(c+7)

i.e. c + 2c - 35 = 0

c+7)(c-5)=0

Because c>0, i.e., c+7>0, the solution is: c=5

1) According to the Pythagorean theorem b = c -a =41 -40 =(41+40)(41-40)=81

b=92)a:b=3:4

c=15 (The cd here should be the height on the hypotenuse ab, right?) ）cd/ac=bc/ab

cd=ab/c=ab/15

Because a b=3 4 a=3 4 b

So a +b =(3 4b) +b =9 16b +b =25 16 b =c

5/4 b=15 b=12 a=9

Thus, cd = ab 15 = 36 5

3) c=50, a=30, then b = c -a = (50+30)(50-30)=1600

b = 40 as above, cd = ab c c = 1200 50 = 24

(1) Knowing the Pythagorean theorem, b 2=c 2-a 2, the root number is found out b=9;

2) Let a=3x, then b=4x, also from the Pythagorean theorem c 2=a 2+b 2, find x=3, you can find a=9, b=12;

Ac*bc=ab*cd is obtained from the invariance of the area of the triangle, and cd=;

3) There is the Pythagorean theorem c 2 = a 2 + b 2 to obtain b = 40, and the triangle area is invariant ac*bc = ab* cd to obtain cd = 24

b=9;Where's the D of the second CD??? The third question cd=24

From the fact that a:b:c=15:8:17 is a right triangle, we can let the equation of a-side 15x, b side 8x, and c-side 17x be.

15x）（8x）/2＝24

0 Solution. x 4 is a side 15 * 4 60, b side 8 * 4 24, c side 17 * 4 68 triangle circumference 60 + 24 + 68 156

Let a 15k, then b 8k, c 17k, and a 2+b 2=c 2, so abc is a right triangle. The area of ABC is 240, i.e. A*B 480, so K2. The circumference of the triangle a+b+c 30+16+34 80

If A 30°, A 1, then C B In RT ABC, the opposite side of angle A is half of the hypotenuse, C = 2, and B = root number 3 with Pythagorean (with sin30°).

If a 45°, a 1, then b c

In RT ABC, the angle A = 45 degrees, the angle B = 45 degrees, and B = 1 is calculated as Pythagorean C = root number 2

If a 30°, a 1, then c=2, b=b root number 3: because c=90°, so c=2a, indicating c=2, according to the Pythagorean theorem, the value of b can be obtained.

If a 45°, a 1, then b 1, c root number 2: because c = 90°, so a = b, b = 1, according to the Pythagorean theorem, the value of c can be obtained.

①tana=a/b=3/4 ∵b=4

a=3 c²=a²+b²

c=5 sinb=b/c=4/5

tana=√5 a/b=√5 a=√5*b。。。

The middle line on the hypotenuse is 3 to get c=6 a +b =36...

Synoptic b= 6 sinb=b c= 6 6

Because A and B are the two roots.

So a+b=7, ab=c+7

Again, the triangle is a right-angled triangle.

So a + b = c

So (a+b) -2ab=c

So the middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse, so the middle line is long.

(1) From the Pythagorean theorem: c 2 = a 2 + b 2 then c 2 = 5 2 + 4 2 = 41, c = 41 (2), the sum of the two sides of the triangle is greater than the third side, so c cannot be equal to 4, there are two cases:

1> third side is c, then according to (1), the third side c = 41;

2>c=5, then the third side is (let a): a 2=c 2-b 2=5 2-4 2=9, then the third side a=3

(the square of a + the square of b).

(the square of a + the square of b).