A topic of high school cosine theorem In △ ABC, B = 30 °, a = 2B, to explore whether this triangle must be a right triangle? Explain the reason

A topic of high school cosine theorem In △ ABC, B = 30 °, a = 2B, to explore whether this triangle must be a right triangle? Explain the reason

It's not the cosine theorem, it's the sine theorem
a/sinA=b/sinB
We get 2sina = SINB = 1, B = 90

If x is greater than 0, y is greater than 0 and 2x + 5Y = 2, then the maximum value of XY is () and x = () y = ()

X is greater than 0, y is greater than 0 and 2x + 5Y = 2
2=2x+5y>=2√10xy
√10xy

Given that XY satisfies the conditions 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, x + 2Y ≤ 8, then z = the maximum of 2x + 5Y

First, we can get two intersections (2,3) (4,2) according to the drawing, and then find the maximum at the point (2,3) according to the slope of 2x + 5Y = 0, and substitute it to get z = 19