Questions: Ratios for Acute Angles 6/10 6/8 8/6 8/10 tan E= sin G= cos G= tan G=

Transcript text: Ratios for Acute Angles $\frac{6}{10}$ $\frac{6}{8}$ $\frac{8}{6}$ $\frac{8}{10}$ $\tan \mathrm{E}=$ $\sin G=$ $\cos G=$ $\tan \mathrm{G}=$

Solution

Solution Steps

Step 1: Identify corresponding sides

Triangle ABD and triangle EFG are similar. Side AB in triangle ABD corresponds to side EF in triangle EFG. Side BD in triangle ABD corresponds to side FG in triangle EFG. Side AD in triangle ABD corresponds to side EG in triangle EFG.

Step 2: Set up ratios

The ratios of corresponding sides in similar triangles are equal. The possible ratios for the acute angles are formed by comparing the lengths of the sides within each triangle. In triangle EFG, the sides are EF = 6, FG = 8, and EG = 10. So the possible ratios are 6/8, 8/6, 6/10, and 8/10. Since triangle ABD is smaller, we can also calculate ratios within that triangle. We would need to calculate the length of AD first using the Pythagorean theorem.

Step 3: Determine available ratios from the options provided

The given options are 6/10, 6/8, 8/6, and 8/10. All of these are valid ratios for the acute angles of triangle EFG.