In angle ABC, Ab=1 and BC=100, which of the following must be true about the angles

a) The measure of angle A is the greatest
b) The measure of angle B is the greatest
c) The measure of angle a and b are equal
d) The measure of angle c is the greatest
e) The measure of angle c is the least

The answer was E. I thought the answer was either A or E, but wasnt that both true? Angle A was the greatest and angel C was also the least?

- - - A.
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B . . . . . . . . . . . . . . ..
. . . .. . . . . . . .. . . . . . . . . . C

B is 90°.......since AB = 1 & BC = 100, let's use a Pythagorean theorem as the following:

AB^2 + BC^2 = AC^2
1^2 + 100^2 = AC^2
1 + 10000 = AC^2
10001 = AC^2
√(10001) = AC

let's find the angle A as :
sin(θ) = BC/AC
sin(θ) = 100/√(10001)
θ = sin^-1( 100/√(10001) )
θ = 89.43°

Let's find the angle C as :
sin(θ) = AB/AC
sin(θ) = 1/√(10001)
θ = sin^-1( 1/√(10001) )
θ = 0.5729° <===== it is the least

welcome :)

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