CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If two angles of ABC are 45° and 60°, then the ratio of the smallest and the greatest sides are


Open in App
Solution

Finding the ratio of smallest and greatest sides:

According to the property of a triangle greatest side of a triangle is opposite to its greatest angle.

And also, the smallest side of a triangle is opposite to its smallest angle.

Given two angles 45°, 60° then the third angle is

180°-45°+60°=75°

Smallest angle is 45° and the largest angle is 75°

By sine rule

asinA=bsinB=csinC

Required ratio =sin45°sin75°

=123+122[sin75°=3+122]=23+1

=23+1×3-13-1[byrationalizing]=23-132-1[(a+b)(a-b)=a2-b2]=23-13-1=3-1

Hence, the ratio of the smallest and the greatest sides is 3-1.


flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle Sum Property
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon