In the RT triangle ABC, ∠ C = 90 °. (1) given a = b = 5, find C; (2) known a = 1, C = 2, find B; (3) known C = 17, B = 8, find a; (4)

（1）
c^2=a^2+b^2=5^2+5^2=50
c=5*2^1/2
(2)b^2=c^2-a^2
=2^2-1^2=4-1=3
b=3^1/2
(3)a^2=c^2-b^2
=17^2-8^2
a=15

In the RT triangle ABC, the angle c = 90 degrees, if C = 13, a = 5, then B= This depends on whether 13 is a right angle side, so there are two cases: C is an oblique edge, B = 12; C is a right angle side, B = radical (169 + 25) = radical 194

In a right triangle, if there is no special explanation, the opposite side of angle a is a and the opposite side of angle c is C
Angle c = 90 degrees, so C is bevel
According to the Pythagorean theorem, B = √ (13? - 5?) = 12
This is my conclusion after meditation,
If you can't ask, I will try my best to help you solve it~
If you are dissatisfied and willing, please understand~

In the RT triangle ABC, given that the angle c is equal to 90 degrees, the angle B is equal to 50 degrees, and ab is equal to 10 degrees, then what is the length of BC

BC=ABsin50°≈7.66

In △ ABC, a = 45 ° C = 30 ° C = 10 cm, find a, B and B

∵ in ᙽ ABC, a = 45 ° C = 30 ° C = 10 cm,
∴B=180°-（A+C）=105°
By sine theorem a
sinA＝c
Sinc, a = C · Sina
sinC=10•sin45°
sin30°=10
2cm．
Similarly, B = C · SINB can be obtained
sinC=10•sin105°
sin30°=5(
6+
2)cm．
To sum up, a = 10
2cm，b=5(
6+
2)cm，B=105°．

The triangular a, B, C and area s of △ ABC satisfy the relationship: S = C2 - (a-b) 2 and a + B = 2. Find the maximum value of area s

From cosine theorem C2 = A2 + b2-2abcosc and area formula s = 1
The substitution condition of 2bsinc
S = C2 - (a-b) 2 = A2 + b2-2abcosc - (a-b) 2, i.e. 1
2absinC=2ab（1-cosC），
∴1−cosC
sinC=1
Let 1-cosc = k, sinc = 4K (k > 0)
The results showed that (2) k = 1 + 2ck = 1
17，
∴sinC=4k=8
Seventeen
∵ a > 0, b > 0, and a + B = 2,
∴S=1
2absinC=4
17ab≤4
17•(a+b)2
2=8
If and only if a = b = 1, Smax = 8
17．

In △ ABC, ∠ a - ∠ B = 36 °, C = 2 ∠ B, then ∠ a = 3_ ，∠B= _ ，∠C= ___ .

From the meaning of the title
∠A-∠B=36°
∠A+∠B+∠C=180°
∠C=2∠B ，
The solution
∠A=72°
∠B=36°
∠C=72° ，
So the answer is 72 degrees, 36 degrees and 72 degrees

If a is the minimum angle in △ ABC, how many sine, cosine and tangent of 3a, 2a, a / 2 must be positive

A must be less than 60 degrees (this can be proved by the method of proof to the contrary, if it is greater than 60 degrees, then the inner angle of the triangle is greater than 180 degrees), then 3A must be less than 180 degrees, 2A must be less than 120 degrees, and a / 2 must be less than 30 degrees
The sine of 3a, the sine of 2a, the sine, cosine and tangent of a / 2 must be positive, so there are five altogether

In the plane rectangular coordinate system, the point P (4, y) is in the first quadrant, and the angle between OP and the positive half axis of X axis is 60 °, then the value of Y is

It can be calculated by tan or Pythagorean theorem

If the angle of Y in the first quadrant is in the right angle of P, then it is in the x-axis I want it today

tan60°=y/4
So y = 4 Tan 60 ° = 4 root sign 3

In the plane rectangular coordinate system xoy, the point P (4, y) is in the first quadrant, and the angle between OP and the positive half axis of X axis is 60 °, then the value of Y is___ .

As shown in the figure
∵OA=4，PA=y，
∴tan60°=PA
OA，
∴PA=OA•tan60°=4×
3=4
3．

In the RT triangle ABC, ∠ C = 90 °. (1) given a = b = 5, find C; (2) known a = 1, C = 2, find B; (3) known C = 17, B = 8, find a; (4)