Question

Please help!!

Law of sines: What is the approximate perimeter of the triangle? Use the law of sines to find the answer.
A. 4.6 units
B. 5.7 units
C. 6.9 units
D. 9.2 units

Answer 1

Hello!

The Law of Sines states, sin A / a = sin B / b = sin C / c. For this problem, we just need to find the other two sides of this triangle.

Let's assign variables. Angle J can be sin A, angle K can be sin B, and angle L can be sin C. Opposite those angles are their corresponding sides. So line KL is a, line JK is c, and line JL is b.

Let's find the other angle measure. Since all triangles are equal to 180 degrees, we can subtract 67 and 74 degrees from 180 to get..

180 - 67 - 74 = 39 | The angle of sin A = 39 degrees.

Let's find the measure of line c (line JK).

sin A / a = sin C / c

sin (39) / 2.3 = sin (74) / c (multiply both sides by c)

0.27361... · c = 0.96126.. (divide both sides by 0.27361)

c = 3.513..

The measure of side c is equal to about 3.5 units.

Now lets find the other side! Which is side b (line JL).

sin A / a = sin B / b

sin (39) / 2.3 = sin (67) / b (multiply both sides by b)

0.27361... · b = 0.92050... (divide both sides by 0.27361...)

b = 3.364...

The measure of side b is equal to about 3.4 units.

After finding all the side measures, we can add the three values together to find the perimeter of the triangle.

2.3 units (side a) + 3.4 units (side b) + 3.4 units (side c) = 9.2 units

Therefore, the perimeter of this triangle is choice D, 9.2 units.

Answer 2

Sure. First we say j=2.3 and J=180-67-74=39 degrees.

The Law of Sines says

`(j)/(\sin J)=(k)/(\sin K) = (l)/(\sin L)`

`k = (j)/(\sin J) \sin K= (2.3)/(\sin 39) \sin 67 \approx 3.364`

`l = (j)/(\sin J) \sin L=(2.3)/(\sin 39) \sin 74 \approx 3.513`

The perimeter is the sum of the sides,

`p \approx 2.3 + 3.364 + 3.513\approx 9.177 \approx 9.2`

Choice D.