By approximately how many feet would Celina need to extend the 60-foot side?

Question

The angle opposite the 60-foot side of the garden measures approximately 26.4°. Celina wants to change the shape of the garden. It will still be a right triangle with the 144-foot side as one leg, but she is going to extend the 60-foot side until the angle opposite that side is about 37°.

(Note: sin 37°= 0.60; cos 37°= 0.80; tan 37°= 0.75)

Answer 1

As you mentioned, tan 37°= 0.75. As we know, tan θ = (the side length opposite θ)/(the side length adjacent to θ). As you said, the 144 foot side is adjacent to the 37° angle, and the side that we are extending is opposite of this 37° angle. So, if we say that the length of the opposite side is 60+x, where x is how much we want to extend the side by, we get that tan 37°= 0.75 = (the side length opposite 37°)/(the side length adjacent 37°) = (60+x) ft./(144 ft.)=0.75, so, after some quick algebra, we solve that 60+x=108, so x=48.