Answer:
41.2
Step-by-step explanation:
You want the perimeter of a right triangle with one leg marked 11 and the adjacent angle marked 50°.
Trig functions
The trig functions useful here are ...
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
Tan = Opposite/Adjacent ⇒ Opposite = Adjacent×Tan
In these ratios, "Adjacent" refers to the side adjacent to the marked angle.
Perimeter
The perimeter is the sum of the side lengths:
P = Adjacent + Hypotenuse + Opposite
P = 11 + 11/cos(50°) + 11·tan(50°) = 11(1 + 1/cos(50°) + tan(50°))
P ≈ 41.2 . . . . units
The perimeter is about 41.2 units.
