The picture below shows a right-triangle-shaped charging stand for a gaming system:

Question

The side face of a charging stand is a right triangle labeled ABC. The measure of angle ACB is 90 degrees, and the measure of angle ABC is 55 degrees. The height of the stand is 7 inches.

Which expression shows the length, BC, of the base of the stand? (4 points)

7 over tan 55 degrees

7(cos 55°)

7 over sin 55 degrees

7(tan 55°)

Answer 1

To find the length of the base \( BC \) of the triangle, we can use the relationship between the angles and sides in a right triangle. In this case, we know the height (which is opposite angle \( ABC \)) and we want to find the length of the adjacent side \( BC \).

Given:

• The height \( AB = 7 \) inches (opposite side to angle \( ABC \)).
• \( \angle ABC = 55^\circ \).

We can use the tangent function, which relates the opposite and adjacent sides in a right triangle:

\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}. \]

Here, we want to find \( BC \) (the adjacent side), so we rearrange the equation:

\[ BC = \frac{AB}{\tan(ABC)}. \]

Substituting the values we have:

\[ BC = \frac{7}{\tan(55^\circ)}. \]

Thus, the expression that shows the length \( BC \) of the base of the stand is:

\[ \boxed{\frac{7}{\tan 55^\circ}}. \]