21.
The angle has an opposite side of value 11 and an adjacent side of value x
We can then apply the formula tan 38° = opposite / adjacent
this gives us tan(38) = 11 / x
11/x = tan(38)
11 = x × tan(38)
x = 11 / tan(38)
x ≈ 14.1 (rounded to the nearest tenth)
And then we need to find the length of the hypotenuse, applying the theorem of Pythagoras. Let H be the hypotenuse, then :
H² = 14,1² + 11²
H² = 198,81 + 121
H = √(319,81)
H ≈ 17,9
Finally the area of the triangle will be (17,9 + 11) / 2 = 28,9 / 2 ≈ 14,45
You apply the same thing for 22 and 23
For 22 you use tan 55 = 15 / x
For 23 you use tan 23 = 7 / x
Good Luck !
