Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,851 users

Law of sines?

0 votes

In triangle ΔXYZXY = 14, YZ = 22, and XZ = 26. What is the measure of angle Z to the nearest degree?  

asked Jul 28, 2014 in ALGEBRA 2 by Don_n Rookie

2 Answers

0 votes

We not able to solve in sine rule

XY=z= 14

YZ = x =22

XZ =y =26

Using cosine rule

cosZ = (x^2+y^2-z^2)/2xy

        =(26^2+22^2-14^2)/2*26*22

       =964/1144

       =0.843

Z= 32.6

answered Jul 28, 2014 by bradely Mentor
edited Jul 28, 2014 by bradely

The law of sines states that

XY/sinZ = YZ/sinX = ZX/sinY

So, we need atleast two angles and one side or two sides and one angle required to find the other. Since we don't have the enough data, we can find the angle using Law of sines.

But we can calculate the angle by using Sin function or cosine rule

cosZ = (x^2+y^2-z^2)/2xy

 

XY=z= 14

YZ = x =22

XZ =y =26

Using cosine rule

cosZ = (x^2+y^2-z^2)/2xy

        =(22^2+26^2-14^2)/)2*26*22)

       = 0.842657

Z = cos^-1(0.842657)

Z= 32.578

0 votes

From sine function, sin(z)= opposite/hypotenuse = 14/26

sin(z) = 14/26

z = sin^-1(14/26) = 32.578

answered Jul 28, 2014 by anonymous
edited Jul 28, 2014 by moderator

Related questions

...