#1**+1 **

1) tan(x) = opposite/adjacent so x = tan^{-1}(opposite/adjacent)

Here we have: x = tan^{-1}(5/20)

You can use the calculator on this site to evaluate this (note that atan is the same as tan^{-1}).

2) sin(angle) = opposite/hypotenuse so sin(45°) = 4sqrt(2)/x or x = 4sqrt(2)/sin(45°)

3) Take the "base" to be the 11cm side. The "height" is then given by 9*sin(63°) cm The area is obtained from (1/2)base*height.

Alan Apr 23, 2018