Question 946528

You want to be able to find the sum of the remaining vertical piece and the hypotenuse piece.


x=12
y, unknown
h, unknown hypotenuse


{{{tan(75)=y/12}}}
{{{y=12*tan(75)}}}


Realize, the parts  of x, y, and h form a right-triangle and you can find h using Pythagorean Theorem.


{{{x^2+y^2=h^2}}}
{{{h=sqrt(x^2+y^2)}}}
{{{h=sqrt(144+144*(tan(75))^2)}}}


Now, you want to know the sum of y and h, the full length of the flag pole before it broke.


{{{12*tan(75)+sqrt(144+144*(tan(75))^2)}}}
and should simplify,
{{{highlight(12*tan(75)+12*sqrt(1+(tan(75))^2))}}}


Approximation for the tan function of 75 degrees,
tan(75)=3.7320