Answer:
The correct expression is 7(tan 55°).
Step-by-step explanation:
To find the length of the base BC of the right triangle, you can use trigonometric ratios. In this case, since we know the height (7 inches) and one angle (55 degrees), we can use the tangent ratio.
The tangent ratio in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
So, for angle ABC (55 degrees), we have:
[tex]\[ \tan(55^\circ) = \frac{BC}{7} \][/tex]
To find BC, we rearrange the equation:
[tex]\[ BC = 7 \cdot \tan(55^\circ) \][/tex]
Therefore, the expression that shows the length BC of the base of the stand is [tex]\( 7 \cdot \tan(55^\circ) \).[/tex]
So, the correct expression is 7(tan 55°).
