7 ft tall
Step-by-step explanation:
The shadows formed by the tree and you are similar triangles so the ratios of their legs must be equal to each other. Therefore, we can write
[tex]\dfrac{x}{20\:\text{ft}} = \dfrac{42\:\text{ft}}{120\:\text{ft}}[/tex]
Solving for the height x, we get
[tex]x = \left(\dfrac{42\:\text{ft}}{120\:\text{ft}}\right)(20\:\text{ft}) = 7\:\text{ft}[/tex]
