Construct a triangle ABC in which angle B= 60o,angle C=75o
and the perpendicular from the vertex A to the base BC is 4.5 cm
Dear Student,
Please find below the solution to the asked query:
Given : , B = 60 and C = 75
Using angle sum property of triangle, we have
B + C + A = 180
60 + 75 + A = 180
A = 45
Steps of Construction:
Step 1 : Draw a line BX .
Step 2 : Place the compass on point B and draw an angle of 60 as shown.
Step 3 : Now, open the arc of compass equivalent to 4.5 cm and from point B and from any other point on BX draw an arc at P and Q as shown.
Step 4 : Join P and Q. Now, PQ is a line parallel to BX at an height of 4.5 cm from it.
Step 5 : The point where line BY and PQ meet each other is the point A.
Step 6 : From point A, take the angular bisector of 60 and 120 and draw an angle of 90 as shown by dotted line AZ ( As BAZ = 90 .
Step 7 : Again,take the angular bisector of 90 and draw an angle of 45 as shown BAC = CAZ = 45.Now, the point at which it cuts the BX is point C.
Hence, triangle ABC is the required triangle.
![](https://s3mn.mnimgs.com/img/shared/ck-files/ck_56d59f3dd13fd.jpg)
Hope this information will clear your doubts about Constructions.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given : , B = 60 and C = 75
Using angle sum property of triangle, we have
B + C + A = 180
60 + 75 + A = 180
A = 45
Steps of Construction:
Step 1 : Draw a line BX .
Step 2 : Place the compass on point B and draw an angle of 60 as shown.
Step 3 : Now, open the arc of compass equivalent to 4.5 cm and from point B and from any other point on BX draw an arc at P and Q as shown.
Step 4 : Join P and Q. Now, PQ is a line parallel to BX at an height of 4.5 cm from it.
Step 5 : The point where line BY and PQ meet each other is the point A.
Step 6 : From point A, take the angular bisector of 60 and 120 and draw an angle of 90 as shown by dotted line AZ ( As BAZ = 90 .
Step 7 : Again,take the angular bisector of 90 and draw an angle of 45 as shown BAC = CAZ = 45.Now, the point at which it cuts the BX is point C.
Hence, triangle ABC is the required triangle.
![](https://s3mn.mnimgs.com/img/shared/ck-files/ck_56d59f3dd13fd.jpg)
Hope this information will clear your doubts about Constructions.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards