Check the picture.
Let A be the point where Mr. and Mrs. McClurrie are standing, let B be the base of the tree and C the top of the tree. Let H be the point representing the house.
ABC is a right triangle, with m(BAC)=30°.
so by special triangles, if the length of the hypotenuse is 2x, the length of BC is x, since it is the side opposite to the 30° angle.
by the pythagorean theorem :
[tex](AC)^{2}= (AB)^{2}+(BC)^{2} [/tex]
[tex](2x)^{2}= (25)^{2}+(x)^{2} [/tex]
[tex]4x^{2}= (25)^{2}+x^{2}[/tex]
[tex]3x^{2}= (25)^{2}[/tex]
[tex]x= \sqrt{ \frac{(25)^{2} }{3}}= \frac{25}{ \sqrt{3} }= \frac{25 \sqrt{3} }{3} [/tex]
[tex]\frac{25 \sqrt{3} }{3}=25* \frac{ \sqrt{3} }{3}=25*0.577= 14.43[/tex] (feet)
so even if the tree falls, it falls more than 5 feet away from the house.
Answer: they can wait a few more years.
