You and your classmate are getting some shade on a field trip. Your classmate is 160cm tall. She stands 360 cm from a tree. Her shadow is 90 cm long. How tall is the tree? Show complete working.
Question
You and your classmate are getting some shade on a field trip. Your classmate is 160cm tall. She stands 360 cm from a tree. Her shadow is 90 cm long. How tall is the tree? Show complete working.
Solution
Sure, let's solve this problem using similar triangles.
Step 1: Identify the similar triangles In this case, the similar triangles are formed by your classmate and her shadow, and the tree and its shadow.
Step 2: Set up the proportion The ratio of your classmate's height to her shadow's length should be the same as the ratio of the tree's height to its shadow's length.
So, we can write the proportion as follows:
(classmate's height / classmate's shadow) = (tree's height / tree's shadow)
Step 3: Substitute the given values into the proportion Substitute the given values into the proportion:
(160 cm / 90 cm) = (tree's height / 360 cm)
Step 4: Solve for the unknown Cross-multiply to solve for the tree's height:
160 cm * 360 cm = 90 cm * tree's height
57600 cm^2 = 90 cm * tree's height
Divide both sides by 90 cm to solve for the tree's height:
tree's height = 57600 cm^2 / 90 cm = 640 cm
So, the tree is 640 cm tall.
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