The attached picture has the small triangle, with the tree as one leg of the triangle and the large triangle, with the building as the corresponding leg of that triangle.
In the original picture, the single small line marked in the side are same length (we can call this x) and the double small line marked in the side are of same length (we can call this y).
So as seen in the attached image:
- Small triangle's hypotenuse (side opposite of 90 degree angle) is x and the base is y.
- Similarly for the larger triangle, hypotenuse is 2x and base is 2y.
- Angle labeled a is same for both
- Also we have 2 right angles as shown
Hence, the triangles are similar and the ratio of their sides are also same.
If we take any side (let's take the hypotenuse) and compute the ratio. We have,
[tex]\frac{hypotenuse of small triangle}{hypotenuse of large triangle}= \frac{x}{2x} =0.5[/tex]. This implies that we can multiply 0.5 to any side of larger triangle to get corresponding side of smaller triangle.
So, the building height and tree height are corresponding sides. To get height of tree, we multiply 0.5 to 120 to get 60 as the height of the tree.
[tex]120*0.5=60[/tex] ft
This is the correct answer.
ANSWER: 60 ft
