Question

find the unknown length. write your answer in simplest form.
2.
3.
4.
5.
6.

Explanation:

Step1: Apply Pythagorean theorem (Q2)

For right triangle: $c^2 = 10^2 + 24^2$
$c^2 = 100 + 576 = 676$
$c = \sqrt{676} = 26$

Step2: Apply Pythagorean theorem (Q3)

For right triangle: $c^2 = 7^2 + 24^2$
$c^2 = 49 + 576 = 625$
$c = \sqrt{625} = 25$

Step3: Apply Pythagorean theorem (Q4)

For right triangle: $38^2 = 25^2 + a^2$
$a^2 = 38^2 - 25^2 = 1444 - 625 = 819$
$a = \sqrt{819} = 3\sqrt{91}$

Step4: Apply Pythagorean theorem (Q5)

For right triangle: $18^2 = 12^2 + b^2$
$b^2 = 18^2 - 12^2 = 324 - 144 = 180$
$b = \sqrt{180} = 6\sqrt{5}$

Step5: Apply Pythagorean theorem (Q6)

For right triangle: $51^2 = 50^2 + a^2$
$a^2 = 51^2 - 50^2 = 2601 - 2500 = 101$
$a = \sqrt{101}$

Answer:

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