Question

the equation cos(35°) = \frac{a}{25} can be used to find the length of \overline{bc}. what is the length of \overline{bc}? round to the nearest tenth. 14.3 in. 20.5 in. 21.3 in. 22.6 in.

Explanation:

1. First, solve the equation \(\cos(35^{\circ})=\frac{a}{25}\) for \(a\):

• Recall that \(a = 25\times\cos(35^{\circ})\).
• We know that \(\cos(35^{\circ})\approx0.819\).
• Then \(a = 25\times0.819 = 20.475\approx20.5\).

1. Discipline and sub - field classification:

• This problem involves trigonometric relations in a right - triangle, which falls under the sub - field of Geometry in the Mathematics discipline.

Answer:

Geometry
20.5 in.