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The angles of a triangle are in AP and the ratio of the numbe

Question

The angles of a triangle are in $A P$ and the ratio of the number of degrees in the least to the number of radius in the greatest is $60 : π$ . The smallest angle is

1 5^{0}

3 0^{0}

4 5^{0}

6 0^{0}

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Jack Discussed

The angles of a triangle are in

A P

and the ratio of the number of degrees in the least to the number of radius in the greatest is

60 : π

. The smallest angle is

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Let the angles be

(a - d)^{0}, a^{0}

and

(a + d)^{0}

. Then,

a - d + a + a + d = 180 \Rightarrow 3 a = 180 \Rightarrow a = 60

So, the angles are

(60 - d)^{0}, 6 0^{0}

and

(60 + d)^{0}

18 0^{0} = π^{c} \Rightarrow (60 + d)^{0} = {\frac{π}{180} \times (60 + d)}^{c} = {\frac{( 60 + d ) π}{180}}^{c}

∴

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

\Rightarrow 180 - 3 d = 60 + d \Rightarrow 4 d = 120 \Rightarrow d = 30

∴

the smallest angle =

(60 - 30)^{0} = 3 0^{0}

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Question Text	The angles of a triangle are in $A P$ and the ratio of the number of degrees in the least to the number of radius in the greatest is $60 : π$ . The smallest angle is
Answer Type	Text solution:1
Upvotes	150