RIGHT TRIANGLES
Question:
- a tree 8m high,cast a shadow of 6m long,at the sametime a bamboo pole nearby cast a shadow of 24m.What is the height of the bamboo pole?
Remember:
- Right triangles can be solved by the formula of pythagorean theorem .
- Pythagorean theorem = a²+b² = c² , where a and b are the bases , and c is the hypothenus or the longest side.
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Solution :
First we will solve the first condition:
a = 8 , b = 6 , c = ?
- a² + b² = c²
- (8)² + (6)² = c²
- 64 + 36 = c²
- 100 = c²
- 10 = c
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Check the second pic above :)
Explanation to the second picture:
- it says in the problem that the shadow is 24 so i make the base 24 and just ignore 6.
- x + 10 because it is the hypothenus because we do not know yet the value of x
- x + 8 because it is just taller to the first bamboo tree
I make the sides as expressions for us to be able to solve easily.
a = 8+x , b = 24 , c = x + 10
Solve using the pythagorean formula:
- a² + b² = c²
- (8+x)² + (24)² = (x+10)²
- 64+16x+x² + 576 = x²+20x+100
- x²-x²+16x-20x+640-100 = 0
- -4x+540 = 0
- -4x = -540
- x = -540 ÷ -4
- x = 135
Substituting the value of x :
a = 8 + 135 = 143
b = 24
c = 145
Checking :
- a²+b² = c²
- (143)²+(24)² = (145)²
- 20449 + 576 = 21025
- 21025 = 21025 ✔️
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Check the third picture :)
FINAL ANSWER
- The bamboo tree has a height of 143meters
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