Question

Have no clue with these 2 please help!!

Answer 1

SOH CAH TOA

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

Answer 2

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

Hope this helps :)