Problem 1 :
The figure shows a right triangle. Find the approximate length of the hypotenuse to the nearest tenth. Check your answer for reasonableness.
Problem 2 :
The figure shows a right triangle. Find the approximate length of the hypotenuse to the nearest tenth. Check your answer for reasonableness.
1. Answer :
Step 1 :
Find the length of each leg.
The length of the vertical leg is 4 units.
The length of the horizontal leg is 2 units.
Step 2 :
Let a = 4 and b = 2 and c represent the length of the hypotenuse.
Because a and b are legs and c is hypotenuse, by Pythagorean Theorem, we have
a^{2} + b^{2} = c^{2}
Step 3 :
Substitute a = 4 and b = 2 in (a^{2} + b^{2} = c^{2)} to solve for c.
4^{2} + 2^{2} = c^{2}
Simplify.
16 + 4 = c^{2}
20 = c^{2}
Take the square root of both sides.
√20 = √c^{2}
√20 = c
Step 4 :
Find the value of √20 using calculator and round to the nearest tenth
4.5 ≈ c
Step 5 :
Check for reasonableness by finding perfect squares close to 20.
√20 is between √16 and √25, so 4 < √20 < 5.
Since 4.5 is between 4 and 5, the answer is reasonable.
The hypotenuse is about 4.5 units long.
2. Answer :
Step 1 :
Find the length of each leg.
The length of the vertical leg is 4 units.
The length of the horizontal leg is 5 units.
Step 2 :
Let a = 4 and b = 5 and c represent the length of the hypotenuse.
Because a and b are legs and c is hypotenuse, by Pythagorean Theorem, we have
a^{2} + b^{2} = c^{2}
Step 3 :
Substitute a = 4 and b = 5 in (a^{2} + b^{2} = c^{2}) to solve for c.
4^{2} + 5^{2} = c^{2}
Simplify.
16 + 25 = c^{2}
41 = c^{2}
Take the square root of both sides.
√41 = √c^{2}
√41 = c
Step 4 :
Find the value of √41 using calculator and round to the nearest tenth
6.4 ≈ c
Step 5 :
Check for reasonableness by finding perfect squares close to 41.
√41 is between √36 and √49, so 6 < √41 < 7.
Since 6.4 is between 6 and 7, the answer is reasonable.
The hypotenuse is about 6.4 units long.
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