Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
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.

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.