Basically, Sin. = opposite/hypotenuse Cos. = adjacent/ hypotenuse Tan. = opposite/ adjacent *adjacent = side next to angle __, hypotenuse = side opposite the right angle aka longest side.
tan. p = opposite/adjacent. RQ is opposite of angle p, so 35 would be the opposite. PR is adjacent to angle P, so 12 would be the adjacent. Notice how PQ is also adjacent is angle P, but it CANNOT be THE adjacent in the ratio because it is THE hypotenuse.
tan. q = opposite/adjacent PR is opposite to angle p, so 12 would be the opposite. RQ is adjacent to angle p, so 35 would be the adjacent.
Final answer: tan. p = 35/12, tan. q = 12/35 *fun fact - these ratios are reciprocals
Answers: Question 1: second option : tan P = 35 / 12 and tan Q =12 /35 Question 2: last option: sin A = 12 /13 and cos A = 5 / 13
Explanation: In a right-angled triangle, special trig functions can be applied. These functions are as follows: sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent
Now, let's see what we have here
question (1): Part (a): θ = P opposite = 35 adjacent = 12 tan P = opposite / adjacent = 35 / 12 Part (b): θ = Q opposite = 12 adjacent = 35 tan Q = opposite / adjacent = 12 /35
question (2): Part (a): θ = A opposite = 12 hypotenuse = 13 sin A = opposite / hypotenuse = 12 /13 Part (b): θ = A adjacent = 5 hypotenuse = 13 cos A = adjacent / hypotenuse = 5 / 13
