In the triangle PQR , PQ = 8, PR = 7 and RQ = 9 Find the size of the largest angle of the triangle. 

2 Answers | Add Yours

embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Angle P is largest as it is opposite the largest side. Use the Law of Cosines to find angle P:




`m/_P=cos^(-1)(2/7)~~73.4^@` .

The area of a traingle can be found if you know two sides and the included angle using `"Area"=1/2 ab sinC`

So `"Area"=1/2(8)(7)sin(73.4)~~26.83` square units.


Largest angle is P with measure 73.4 degrees; the area of the triangle is approximately 26.83 square units


llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

The law of sines require that the angle opposite to the largest side must be the largest angle.

Here, largest side is QR.

So, `angleP` must be the largest.

It can be found out using the law of cosines. Thus,


`rArr angleP=arccos(0.2857)=73.4^o`

Area of the triangle can be obtained by Heron's formula.

Here `s=(8+7+9)/2=12 ` units

Area A=`sqrt(12*(12-8)(12-7)(12-9))` sq. units

`=sqrt(12*4*5*3)=sqrt720 ` sq. unit

`=26.83 ` sq. units

Therefore, the measure of the largest angle of the triangle is 73.4 degrees and its area is 26.83 sq. units.


We’ve answered 317,411 questions. We can answer yours, too.

Ask a question