In a triangle abc, with angles a, b, and c and sides ab, bc, and ac, angle b is a right (90°) angle. if the sin of angle a is 0.5 and side bc is 8 inches long, what is the length of side ac?

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

In the following diagram it is given that dec,ab || dc, ad || eb, and ad is congruent to bc. a)why isn't abc a parallelogram even though it has a pair of parallel sides and a pair of congruent sides b)explain why be must be congruent to bc. further explain what type of triangle this makes triangle abc and what it tells you about angle 1 and angle 2c) finally why must angle 3 be congruent to angle 1? further, explain why we know that angle 3 is congruent to angle 2

The map shows the location of the airport and a warehouse in a city. though not displayed on the map, there is also a factory 112 miles due north of the warehouse.a truck traveled from the warehouse to the airport and then to the factory. what is the total number of miles the truck traveled?