First I have to figure out how far the tree is from me. I know that it is 10 ft. tall . If I look up at the tree at a 45° the top of it looks like it's about 14 ft away from me.
If I use sine I get 12/17 which is equal to about .7 and if I multiply that by 17 I get the distance of me from the tree which is 12 feet. I can check my answer by using cosine. I get 12/17 multiplied by 17 which equals 12 again. If I use tangent I get 12/12 and when I multiply that 12 I get 12.
If I wanted to find the measure of angle β, I would find the inverse cosine which is 45°. In conclusion I need to shoot the arrow 12 feet in order to hit the target.