For a craft project, Jackie cuts the two triangles described below out of fabric. Find the length of CE¯¯¯¯¯¯¯¯. In triangle CDE, CD¯¯¯¯¯¯¯¯=7 cm, CE¯¯¯¯¯¯¯¯=(4z+7) cm, ∡C=48°, and ∡E=82°. In triangle TUV, UV¯¯¯¯¯¯¯¯=(13z−20) cm, UT¯¯¯¯¯¯¯=7 cm, ∡U=48°, and ∡V=82°.

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Given:

In triangle CDE, CD=7 cm, CE=(4z+7) cm, ∡C=48°, and ∡E=82°.

In triangle TUV, UV=(13z−20) cm, UT=7 cm, ∡U=48°, and ∡V=82°.

To find:

The length of CE.

Solution:

In triangle CDE and triangle UTV,

      (Given)

      (Given)

      (Given)

Two angles and a non -included side are equal in both triangle. So, both triangles are congruent by AAS postulate.

                (CPCTC)

Divide both sides by -9.

Now,

Therefore, the length of CE is 19 cm.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2