Two angles of a triangle are 70° and 80° The vertices of the triangle are on a circle of radius 3.5cm construct the triangle.

Asked by lijimoljayan | 12th Sep, 2021, 06:26: PM

Expert Answer:

This construction of triangle is made using the sine rule of Triangle as given below

begin mathsize 14px style fraction numerator a over denominator sin left parenthesis A right parenthesis end fraction space equals space fraction numerator b over denominator sin left parenthesis B right parenthesis end fraction space equals space fraction numerator c over denominator sin left parenthesis C right parenthesis end fraction space equals space 2 R end style
 
where a , b and c are sides of triangle .  A, B and C are angles as shown in figure. R is radius of circumcircle.
 
Angles of triangle are ,  A = 30 , B = 70o and C = 80o 
 
a = 2R sin(A) = 7 × sin(30) = 3.5 cm
 
b = 2R sin(B) = 7 × sin(70) = 6.6 cm
 
c = 2R sin(C) = 7 × sin(80) = 6.9 cm
 
To get the required triangle , we construct the triangle with sides 3.5 cm, 6.6 cm and 6.9 cm
 

 

Answered by Thiyagarajan K | 16th Sep, 2021, 10:50: PM