Question

The angles of a triangle are in A.P. and the number of degrees in the least to the number of radians in greatest is 60 to . The angles in degree are
(1) 60°, 60°, 60° (2) 30°, 60°, 90° (3) 45°, 60°, 75° (4) 15°, 60°, 105

Answer 1

WELL you have to figure the amount of degree in least to the number of radiant least to greatest you need to find

Answer 2

ok before i explain this , plz dont bash me about giving answer, i am just giving explanation.

Answer 3

let the angles of the triangle be \[(a-z)^{o}, a^o, (a+z)^o \] then \[(a-z)+a+(a+z)=180\rightarrow 3a=180^o \rightarrow a=60\] so the angles are are\[(60-z)^o, 60^o, (60+z)^o \] what we know is that (60-z) is the smallest angle and (60+z) is the greatest angle.

so greatest angle =\[(60+z)^o =\left\{ (60+z) \times \frac{ \pi }{ 180 } \right\}^c \] In the question it is given that
(number of degrees in the least angle)/(number of radians in the greatest angle )\[=\frac{ 60 }{ \pi }\]
so \[\frac{ (60-z) }{ (60+z) \times \frac{ \pi }{ 180 } }=\frac{ 60 }{ \pi }\rightarrow 3(60-z)=(60+z)\rightarrow 120=4z \rightarrow z=30\]
Please sub in values:

Hence the angles are \[(60-z)^o , 60^o ,(60+z)^o i.e. ....\]

Answer 4

@NikhilNaidu: Most of the rest of us are not going to understand your abbreviation, A. P., at least not in a way that will help them help you with this problem. Please spell out what A. P. represents.

Unfortunately, your "the number of degrees in the least to the number of radians in greatest is 60 to ." is also difficult to follow. Does the original problem really mix radian measure and degree measure in this one problem? What I think you meant here is "the largest angle is 60 degrees greater than the smallest." Please clarify your meanings.