Question

A tree casts a shadow 27 m long. At the same time, the shadow cast by a 66-cm tall statue is 56 cm long. Find the height of the tree to the nearest tenth of a meter?

Answer 1

$\frac{height _{1} }{shadow_{1}} = \frac{height _{2} }{shadow_{2}}$

$\frac{height _{1} }{27m} = \frac{66cm}{56cm}$

$\frac{height _{1} }{2700cm} = \frac{66cm}{56cm}$

$2700*66=56*h _{1}$

$178200=56h _{1}$

$3182.1cm=h _{1}$

$\frac{3182.1cm}{1000cm} = 3.2m$

$height:3.2m$

Answer 2

As long as everything is on level ground with uniform elevation, and everything happens at the same time of day (with the sun at the same height in the sky) ... 

(66cm statue) / (56cm shadow) = (height of tree, meters) / (27m shadow)

Multiply each side of the equation by (27m) :

height of tree = (66 cm) x (27m) / (56cm) = 31.82 meters or 31.8 meters