Question 1153777
<br>
x = height of tree
x+1 = distance from Lucy to top of tree
x-71 = distance from Lucy to base of tree<br>
Assuming the ground is level (NOT a good assumption in the location of the General Sherman tree!), then the three lengths form a right triangle.<br>
{{{(x+1)^2 = x^2+(x-71)^2}}}
{{{x^2+2x+1 = x^2+x^2-142x+5041}}}
{{{0 = x^2-144x+5040}}}
{{{0 = (x-60)(x-84)}}}<br>
{{{x = 60}}} or {{{x=84}}}<br>
x=60 makes the distance from Lucy to the base of the tree negative, so that solution makes no sense.<br>
ANSWER: The height of the tree is x = 84m.<br>