Q.10 The
measures of the angles of
of a
triangle are in A.P. and the greatest is
5 times the smallest (least). Find the
angles in degree and radian.
Answers
Answer:
Angles respectively will be 20 ° , 60° and 100°
Step-by-step explanation:
MOST IMPORTANT PROPERTY TO BE USED HERE IS THAT THE SUM OF ANGLES OF A TRIANGLE IS 180° .
NOW , considering it to be in A.P . let us assume first angle to be equal to "a" . Then , the third and the largest is 5a . Now , let the second angle be equal to a+d . Using the properties of an AP , we get that , (a+d - a ) = 5a - (a +d)
This gives , d = 4a -d ------ (1)
Also , a + (4a-d) + a + 5a = 180
11a - d = 180 --------- (2)
From 1 , d = 2a .
putting this in 2 .
a = 20 °.
d = 40°
So angles respectively will be 20 ° , 60° and 100° . Now you can convert the same into radians . Hence will be your answer .
Answer:
Step-by-step explanation:
MOST IMPORTANT PROPERTY TO BE USED HERE IS THAT THE SUM OF ANGLES OF A TRIANGLE IS 180° .
NOW , considering it to be in A.P . let us assume first angle to be equal to "a" . Then , the third and the largest is 5a . Now , let the second angle be equal to a+d . Using the properties of an AP , we get that , (a+d - a ) = 5a - (a +d)
This gives , d = 4a -d ------ (1)
Also , a + (4a-d) + a + 5a = 180
11a - d = 180 --------- (2)
From 1 , d = 2a .
putting this in 2 .
a = 20 °.
d = 40°
So angles respectively will be 20 ° , 60° and 100° . Now you can convert the same into radians . Hence will be your answer .