Question

find bc.
triangle image with right angle at d, bd=4, angle at b is 66°
write your answer as an integer or as a decimal rounded to the nearest tenth.
bc =
submit

Explanation:

Step1: Identify the triangle type

Triangle \( BCD \) is a right - triangle with \( \angle D = 90^{\circ} \), \( BD = 4 \), and \( \angle B=66^{\circ} \). We want to find the length of \( BC \). In a right - triangle, we can use trigonometric ratios. The cosine of an angle in a right - triangle is defined as the adjacent side divided by the hypotenuse. For \( \angle B \), the adjacent side is \( BD \) and the hypotenuse is \( BC \). So, \( \cos(B)=\frac{BD}{BC} \).

Step2: Solve for \( BC \)

We know that \( \cos(66^{\circ})\approx0.4067 \) and \( BD = 4 \). From the formula \( \cos(B)=\frac{BD}{BC} \), we can re - arrange it to solve for \( BC \): \( BC=\frac{BD}{\cos(B)} \). Substitute \( BD = 4 \) and \( \cos(66^{\circ})\approx0.4067 \) into the formula: \( BC=\frac{4}{\cos(66^{\circ})}\approx\frac{4}{0.4067}\approx9.8 \)

Answer:

\( 9.8 \)