Question 1120894
your triangle looks like this:


<img src = "http://theo.x10hosting.com/2018/080511.jpg" alt="$$$" >


TU = 11 cm.


TH = 120% of HU.


if we let x = HU, then 1.2x = TH


TH + TU = 11 results in 1.2x + x = 11 which results in 2.2x = 11.


solve for x to get x = 11/2.2 = 5


that makes 1.2x = 1.2 * 5 = 6


since 1.2x = TH, we have TH = 6 and we have HU = 5.


the area of triangle STH is equal to 21 cm^2.


area of a triangle is equal to 1/2 * base * height.


the area is 21 and the base is 6.


formula becomes 21 = 1/2 * 6 * H, where H is equal to SH.


solve for H to get H = 21 * 2 / 6 = 7.


the height of the triangle is equal to SH which is equal to 7.


we are looking for the measure of angle TSU.


the measure of angle TSH is equal to arctan(TH / SH which is equal to arctan(6/7).


that makes angle TSH equal to 40.60129465 degrees.


the measure of angle HSU is equal to arctan(HU/SH) which is equal to arctan(5/7).


that makes angle HSU equal to 35.53767779.


angle TSU is the sum of these two angle.


that makes angle TSU equal to 40.60129465 + 35.5376777 = 76.13897244 degrees.


that's your solution.