Question

Please answer right away

Answer 1

Answer:

6.13

Step-by-step explanation:

Using Sine Law we know that

$\dfrac{a}{SinA}=\dfrac{b}{SinB}=\dfrac{c}{SinC}$

Using your figure let's assign sides and angles:

A=? B = 60° C = 70°

a = 5 b = ? c = x

If we put that into our formula:

$\dfrac{5}{Sin?}=\dfrac{?}{Sin60}=\dfrac{x}{Sin70}$

Notice that we have too many unknowns. We need to complete at least one ratio to do this, so how do we do this?

Notice we have 2 angles given, so we solve for the third angle. The sum of all angles in any triangle is always 180°

∠A + ∠B + ∠C= 180°

∠A + 60° + 70° = 180°

∠A + 130° = 180°

∠A = 180° - 130°

∠A = 50°

Now we can use this to solve for x.

$\dfrac{5}{Sin50}=\dfrac{x}{Sin70}\\\\\dfrac{(5)(Sin70)}{Sin50} = x\\\\\dfrac{4.6985}{0.7660}=x\\\\6.1338 =x$

So the closest answer would be 6.13

Answer 2

Answer:

The correct answer option is 6.13.

Step-by-step explanation:

We are given a scalene triangle which has no equal side and we are to find the unknown side length x.

Since the total measure of angles of a triangle is 180°, so we can find the measure of the unknown angle.

180° - 70° + 60° = 50°

Now we can use the sine formula to find the value of x.

$\frac{x}{sin70} =\frac{5}{sin50}$

$x=\frac{5}{sin50} \times sin70$

$x=6.13$