Question 210462
1) Use the Pythagorean theorem:
{{{c^2 = a^2+b^2}}} Substitute c = 17, a = 8, and b = the height of the flagpole.
{{{17^2 = 8^2+b^2}}} Solve for b.
{{{ 289 = 64+b^2}}} Subtract 84 from both sides.
{{{225 = b^2}}} Take the square root of both sides.
{{{15 = b}}}
The flagpole is 15 meters high.
2) Use the similar right triangles method: Let h = the building height.
{{{3/1 = h/12}}} 
{{{h = 12*3}}} 
{{{h = 36}}}meters.
3) Use the tangent function: Let d = the distance from the base of the lighthouse to the point on the beach.
The tangent of the angle of depression (8 degs) is:
{{{tan(8) = 20/d}}}
{{{d = 20/tan(8)}}}
{{{d = 142.31}}} meters.
4) Let the side of the square = s, then, using the Pythagorean theorem:
{{{(9sqrt(2))^2 = s^2+s^2}}}
{{{81*(2) = 2s^2}}} Divide both sides by 2.
{{{81 = s^2}}} Take the square root of both sides.
{{{s = 9}}}