Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Answer:
(d) 9.2 units
Step-by-step explanation:
Given ∆JKL with K=67°, L=74°, and KL=2.3, you want the perimeter of the triangle.
Law of sines
The law of sines tells you the relationship between the sides and angles:
[tex]\dfrac{JK}{\sin(L)}=\dfrac{KL}{\sin(J)}=\dfrac{LJ}{\sin(K)}[/tex]
To use this relation, we need to know the angle opposite the given side.
∠J +∠K +∠L = 180°
∠J +67° +74° = 180°
∠J = 39° . . . . . . . . . . . . subtract 141° from both sides
Now, we can write ...
[tex]\dfrac{JK}{\sin(74^\circ)}=\dfrac{2.3}{\sin(39^\circ)}=\dfrac{LJ}{\sin(67^\circ)}[/tex]
Side lengths
Solving this equation for JK and LJ, we have ...
[tex]JK=2.3\cdot\dfrac{\sin(74^\circ)}{\sin(39^\circ)}\\\\\\LJ=2.3\cdot\dfrac{\sin(67^\circ)}{\sin(39^\circ)}\\\\\\P=KL +JK +LJ\\\\\\P=2.3+2.3\cdot\dfrac{\sin(74^\circ)}{\sin(39^\circ)}+2.3\cdot\dfrac{\sin(67^\circ)}{\sin(39^\circ)}\\\\\\P=2.3\left(1+\dfrac{\sin(74^\circ)+\sin(67^\circ)}{\sin(39^\circ)}\right)\approx 9.177[/tex]
The perimeter of the triangle is about 9.2 units, choice D.

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.