On which triangle can the law of cosines be applied once to find an unknown angle measure? law of cosines: a2 = b2 + c2 – 2bccos(a)

options are in the pics

The correct option is 4.

Explanation:

The formula of law of cosine is,

Where a,b,c are sides of the triangle and A is the interior angle of vertex A.

Reason for correct option:

From the above formula we can easily conclude that to find an unknown angle measure we need the length of all sides of the triangle.

In figure 4 all sides are given, so the correct option is 4.

Reason for incorrect option:

In figure 1,2 and three all sides are not known, so we can apply the cosine rule to mind the unknown angle measure.

Therefore option 1,2 and 3 are incorrect.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c