Problem

Triangle BAC was dilated from triangle BDE at a scale factor of 2. What proportion proves that \( \cos \angle D=\cos \angle A \) ?

Answer

Expert–verified
Hide Steps
Answer

\( \cos \angle D = \cos \angle A \) since \( \frac{BD}{DE} = \frac{AB}{AC} \)

Steps

Step 1 ：\( \triangle BDE \sim \triangle BAC \) , scale factor = 2

Step 2 ：\( \frac{DE}{AC} = \frac{BD}{AB} = \frac{BE}{BC} = \frac{1}{2} \)

Step 3 ：\( \cos \angle D = \frac{BD}{DE} , \cos \angle A = \frac{AB}{AC} \)

Step 4 ：\( \cos \angle D = \cos \angle A \) since \( \frac{BD}{DE} = \frac{AB}{AC} \)

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More