Final answer:
Using the concept of similar triangles, we determine the ratio of the height to the shadow of the pole and apply it to the tree, concluding that the tree is 15 meters tall.
Step-by-step explanation:
To solve for the height of the tree, we will use similar triangles because the sun's rays create similar triangles between the pole and its shadow and the tree and its shadow. The ratio of the height of the pole to its shadow will be the same as the ratio of the height of the tree to its shadow.
The ratio for the pole is 5 meters to 4 meters. So for every 4 meters of shadow, there is a height of 5 meters.
For the tree, we know the shadow is 12 meters. Using the ratio from the pole, we can set up a proportion:
5 / 4 = Height of Tree / 12. To find the height of the tree, we multiply both sides of the equation by 12 to isolate the height of the tree:
Height of Tree = (5 / 4) × 12 = 15 meters.
Therefore, the tree is 15 meters tall.
To find the length of the tree, we can use the concept of similar triangles. Let's call the length of the tree 'x'. According to the given information, the pole and its shadow form one pair of similar triangles, and the tree and its shadow form another pair of similar triangles. Using the property of proportionality of corresponding sides of similar triangles, we can set up the following equation:
(5 m/4 m) = (x/12 m)
Cross-multiplying, we get: 4x = 60 m
Dividing both sides by 4, we find that the length of the tree is 15 meters.