Question

GEOMETRY 30 POINTS!!

Answer 1

Answer:

The expression to calculate the side BC is $BC=7\cot 55^\circ.$

Step-by-step explanation:

Notice that this is a problem of trigonometry in right triangles. So, the first step is to identify the data we have and the unknowns.

• The right angle is C.
• The measure of the angle B is $55^\circ$.
• The length of the side AC is 7 in.
• We want to know the length of the side BC.

Then, the questions is: What trigonometrical functions relates the measure of an angle and the sides of a right triangle? The answer is: the tangent.

The formula for the tangent of B is $\tan B =$opposite/adjacent; i.e.

$\tan B = \frac{AC}{BC}.$

Now, isolating the side BC

$BC = \frac{AC}{\tan B}.$

But the reciprocal function of the tangent is the cotangent, then

$BC = AC\cot B.$

Finally, substituting the known values:

$BC = 7\cot 55^\circ.$

Answer 2

In this triangle, $\tan55^\circ=\dfrac{AC}{BC}$, so

$BC=\dfrac7{\tan55^\circ}=7\cot55^\circ$