The angles of a triangle are in A.P. The number of degrees in the least is to be the number of radians in the greatest as . Then the greatest angle is

Question

The angles of a triangle are in A.P. The number of degrees in the least is to be the number of radians in the greatest as $60 : π$ . Then the greatest angle is

Smart Achievers · Accepted Answer

(2)

Let the angles of the triangle be $(a - d) °, a °, (a + d) °$

Their sum is $a - d + a + a + d = 180$

$\Rightarrow 3 a = 180$ $\Rightarrow a = 60$

Again, by the given condition,

$\frac{a - d}{\frac{(a + d) π}{180}} = \frac{60}{π}$ $\Rightarrow \frac{3 (a - d)}{a + d} = 1$

$\Rightarrow 3 a - 3 d = a + d$

$\Rightarrow 2 a = 4 d$ $\Rightarrow$ $a = 2 d$

$∴$ $60 = 2 d$ $∴$ $d = 30$

Hence, the greatest angle $= 60 + 30 = 90 °$

Solution

Q.
The angles of a triangle are in A.P. The number of degrees in the least is to be the number of radians in the greatest as $60 : π$ . Then the greatest angle is

1 $120 °$

2 $90 °$

3 $135 °$

4 $105 °$

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Solution

Q. The angles of a triangle are in A.P. The number of degrees in the least is to be the number of radians in the greatest as 60:π. Then the greatest angle is

1 120°

2 90°

3 135°

4 105°