The three sides a, B and C of triangle ABC satisfy the relation a ^ 2 + B ^ 2 + C ^ 2 + 338 = 10A + 24B + 26c. What triangle is it?

The three sides a, B and C of triangle ABC satisfy the relation a ^ 2 + B ^ 2 + C ^ 2 + 338 = 10A + 24B + 26c. What triangle is it?

A ^ 2 is the square of A
a^2 + b^2 + c^2 + 338 = 10a + 24b + 26c
(a-5)^2 + (b-12)^2 + (c-13)^2 = 0
Because all three terms are greater than or equal to 0, and the sum of the three terms is 0, the three terms must be zero
So a = 5, B = 12, C = 13
And satisfy: A ^ 2 + B ^ 2 = C ^ 2
Therefore, this triangle is RT triangle

C = 2, C = 60 ° and ABC is an acute triangle, find the value range of a + B

According to the sine theorem
c/sinC=a/sinA=b/sinB
That is 2 / sin 60 ° = A / sin a = B / sin (120 ° - a)
So a = 4 √ 3 / 3sina, B = 4 √ 3 / 3sin (120 ° - a)
So a + B = 4 √ 3 / 3sina + 4 √ 3 / 3sin (120 ° - a)
=4√3/3[sinA+sin(120°-A)]
=4√3/3[sinA+sin120°cosA-cos120°sinA]
=4√3/3[sinA+√3cosA/2+sinA/2]
=4√3/3[3sinA/2+√3cosA/2]
=4[√3sinA/2+cosA/2]
=4[sinAcos30°+cosAsin30°]
=4sin(A+30°)
In the acute triangle ABC,
Because 0

In the acute triangle ABC, a = 1, B = 2, find the value range of C

Because it's an acute triangle, so
① If B is the largest edge, then
A & # 178; + C & # 178; > b & # 178;, that is, C & # 178; > 3, C > √ 3
② If C is the largest edge, then
A & # 178; + B & # 178; > C & # 178;, namely C & # 178;