Question

Maricel is programming an archery component of a new video game. In her code, she has created an "auto aim" feature that helps players more easily hit their intended targets.

The code works such that if the player is aimed at
A
AA but instead should be aimed at target
T
TT, the game will automatically adjust the angle at which the arrow is fired directly at
T
TT.
If
A
AA and
T
TT are
15
1515 meters apart in the example below, how many degrees will Maricel's code adjust the shot?
Do not round during your calculations. Round your final answer to the nearest degree.

Answer 1

Step-by-step explanation:

Answer 2

• 12º

Step-by-step explanation:

The angle Marcel's code adjust the shot can be calculated using the cosine law:

`C^2=A^2+B^2-2|A||B|cos(c)`

For the triangle of the figure:

• C = 15m
• A = 50m
• B = 60m
• c = ? (the unknown angle)

Substitute and solve for c:

`(15m)^2=(50m)^2+(60m)^2-2(50m)(60m)cos(c)\\\\\\225=2500+3600-6000cos(c)\\\\6000cos(c)=2500+3600-225=5,875\\\\cos(c)=5,875/6000\approx0.97917\\\\c=arccos(0.97917)\approx12\º`