Question

What is the approximate perimeter of the triangle? Use the law of sines to find the answer. 4. 6 units 5. 7 units 6. 9 units 9. 2 units.

Answer 1

To solve the problem we need to know about Sine Rule.

What is Sine rule?

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

$\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}$

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

The perimeter of the triangle is 9.177 units.

Given to us

• KL = 2.3
• ∠K = 67°
• ∠L = 74°

For ∠J

We know that the sum of all the angles of a triangle is equal to 180°.

∠J + ∠K + ∠L = 180°

∠J + 67° + 74° = 180°

∠J + 141° = 180°

∠J = 39°

Using the Sine Rule,

$\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}$

Substitute the values,

$\dfrac{Sin\ \angle J}{KL} =\dfrac{Sin\ \angle K}{JL} =\dfrac{Sin\ \angle L}{JK}\\\\\\\dfrac{Sin\ \angle J}{2.3} =\dfrac{Sin\ \angle K}{JL} =\dfrac{Sin\ \angle L}{JK}$

For Side JL

$\dfrac{Sin\ \angle J}{2.3} =\dfrac{Sin\ \angle K}{JL}$

$JL =\dfrac{Sin\ \angle K\times 2.3}{Sin\ \angle J}\\\\JL =3.3642$

For Side JK

$\dfrac{Sin\ \angle J}{2.3} =\dfrac{Sin\ \angle L}{JK}$

$JK =\dfrac{Sin\ \angle L\times 2.3}{Sin\ \angle J}\\\\JK =3.513$

The perimeter of the Triangle

Perimeter of the triangle =  JK+KL+JL

                                         = 3.513 + 2.3 + 3.3642

                                         = 9.177

Hence, the perimeter of the triangle is 9.177 units.

Learn more about Sine Rule:

https://brainly.com/question/17289163

Answer 2

Answer:

9.2

Step-by-step explanation:

You would have to round 9.17 to 9.2 which is the correct answer!