Question

lesson 9.3 practice for use with pages 464-469 name: deasia mcdonald
find the unknown length. write your answer in simplest form.

1. right triangle with legs 24, 10, hypotenuse c
2. right triangle with legs 24, 7, hypotenuse c
3. right triangle with legs 6, 2, hypotenuse c
4. right triangle with hypotenuse 38, leg 25, leg a
5. right triangle with hypotenuse 18, leg 12, leg b
6. right triangle with hypotenuse 51, leg 50, leg a

Explanation:

Step1: Apply Pythagorean theorem (Q2)

$c^2 = 7^2 + 24^2$

Step2: Calculate squares and sum (Q2)

$c^2 = 49 + 576 = 625$

Step3: Solve for c (Q2)

$c = \sqrt{625} = 25$

Step4: Apply Pythagorean theorem (Q3)

$c^2 = 2^2 + 6^2$

Step5: Calculate squares and sum (Q3)

$c^2 = 4 + 36 = 40$

Step6: Simplify square root (Q3)

$c = \sqrt{40} = 2\sqrt{10}$

Step7: Rearrange Pythagorean theorem (Q4)

$a^2 = 38^2 - 25^2$

Step8: Calculate squares and difference (Q4)

$a^2 = 1444 - 625 = 819$

Step9: Simplify square root (Q4)

$a = \sqrt{819} = \sqrt{9\times91} = 3\sqrt{91}$

Step10: Rearrange Pythagorean theorem (Q5)

$b^2 = 18^2 - 12^2$

Step11: Calculate squares and difference (Q5)

$b^2 = 324 - 144 = 180$

Step12: Simplify square root (Q5)

$b = \sqrt{180} = \sqrt{36\times5} = 6\sqrt{5}$

Step13: Rearrange Pythagorean theorem (Q6)

$a^2 = 51^2 - 50^2$

Step14: Calculate squares and difference (Q6)

$a^2 = 2601 - 2500 = 101$

Step15: Solve for a (Q6)

$a = \sqrt{101}$

Answer:

1. $c=26$
2. $c=25$
3. $c=2\sqrt{10}$
4. $a=3\sqrt{91}$
5. $b=6\sqrt{5}$
6. $a=\sqrt{101}$