Question 1036188
<pre>Since the entire structure represents a 30-60-90 special triangle, the distance from the boat to the base of the statue (also the SHORTER leg of the triangular structure) is: {{{305 * sqrt(3)/3}}}
Using 305 - h as the height of the statue's base, the shorter leg: {{{305 * sqrt(3)/3}}}, the angle of elevation {{{41.2^o}}} from the boat to the base of the statue, we get h, or height of statue as: {{{highlight_green(matrix(1,2, 150.8433, feet))}}}

<b><u>Different approach</b></u>
The hypotenuse (distance from boat to top of statue) can be derived. As this is a 30-60-90 special right triangle, the hypotenuse is: {{{2(305)( sqrt(3))/3}}}, or {{{610 * sqrt(3)/3}}}
Difference between angles of elevation: 60 - 41.2, or {{{18.8^o}}}
Using height of statue only (h), difference in angles of elevation ({{{18.8^o}}}), the hypotenuse: {{{610 * sqrt(3)/3}}}, the third angle in that triangle ({{{131.2^o}}}), and the law of sines, we get: {{{h/sin (18.8) = ((610 * sqrt(3)/3))/sin (131.2^o)}}}
{{{h * sin (131.2^o) = (610 * sqrt(3)/3) * sin (18.8^o)}}} ------- Cross-multiplying
h, or height of statue = {{{highlight_green(matrix(1,2,((610 * sqrt(3)/3) * sin (18.8^o))/sin (131.2^o) = 150.8433, feet))}}}