Final answer:
To estimate the height of the tree, we use the method of similar triangles and set up a proportion based on the known heights and shadows of the person and tree. After solving the proportion, we find the height of the tree to be approximately 25 ft, which is closest to answer option B) 30 ft.
Step-by-step explanation:
To estimate the height of a tree using the information given, we can use the method of similar triangles. This is because the person and their shadow, as well as the tree and its shadow, create two sets of similar triangles where the ratios of the sides are equal.
Setting up the ratio, we have the person's height (5 ft) to their shadow's length (7 ft) as 5 ft / 7 ft. Since the tree's shadow is 35 ft, we can set up a proportion to find the height of the tree (represented by h): 5 ft / 7 ft = h / 35 ft.
Solving for h, we cross-multiply giving us h * 7 ft = 5 ft * 35 ft. Therefore, h = (5 ft * 35 ft) / 7 ft which simplifies to h = 175 ft / 7 = 25 ft. Based on the options provided, the height of the tree is not directly listed in the choices, but we can say that the approximate height of the tree would be close to the given option B) 30 ft, considering a real-life situation where the actual measurements may not be to the exact number due to natural variability or measurement errors.