Question

1. find the length of the missing side. (diagrams are not drawn to scale.) this must be done on separate paper.

a. a right triangle with legs 5 and 12, and hypotenuse a.
b. a right triangle with hypotenuse 29, one leg 21, and the other leg c.
c. a right triangle with legs 6 and 8, and hypotenuse x.
d. a right triangle with hypotenuse 25, one leg 24, and the other leg b.
e. a right triangle with legs 8 and 15, and hypotenuse s.
f. a right triangle with hypotenuse 25, one leg 20, and the other leg w.
g. a right triangle with legs 63 and k, and hypotenuse 65.
h. a right triangle with legs 78 and 160, and hypotenuse y.
i. a right triangle with legs 112 and 66, and hypotenuse d.
j. a right triangle with legs 35 and 12, and hypotenuse a.
k. a right triangle with hypotenuse 5, one leg 3, and the other leg e.
l. a right triangle with hypotenuse 26, one leg 10, and the other leg z.

Explanation:

⚡ Using what you learned: the pythagorean theorem and its converse

Step 1: Solve triangle a.

$$ 5^2 + 12^2 = a^2 $$

$$ 25 + 144 = a^2 $$

$$ 169 = a^2 $$

$$ a = 13 $$

Step 2: Solve triangle b.

$$ c^2 + 21^2 = 29^2 $$

$$ c^2 + 441 = 841 $$

$$ c^2 = 400 $$

$$ c = 20 $$

Step 3: Solve triangle c.

$$ 6^2 + 8^2 = x^2 $$

$$ 36 + 64 = x^2 $$

$$ 100 = x^2 $$

$$ x = 10 $$

Step 4: Solve triangle d.

$$ b^2 + 24^2 = 25^2 $$

$$ b^2 + 576 = 625 $$

$$ b^2 = 49 $$

$$ b = 7 $$

Step 5: Solve triangle e.

$$ 8^2 + 15^2 = s^2 $$

$$ 64 + 225 = s^2 $$

$$ 289 = s^2 $$

$$ s = 17 $$

Step 6: Solve triangle f.

$$ w^2 + 20^2 = 25^2 $$

$$ w^2 + 400 = 625 $$

$$ w^2 = 225 $$

$$ w = 15 $$

Step 7: Solve triangle g.

$$ k^2 + 63^2 = 65^2 $$

$$ k^2 + 3969 = 4225 $$

$$ k^2 = 256 $$

$$ k = 16 $$

Step 8: Solve triangle h.

$$ 78^2 + 160^2 = y^2 $$

$$ 6084 + 25600 = y^2 $$

$$ 31684 = y^2 $$

$$ y = 178 $$

Step 9: Solve triangle i.

$$ 112^2 + 66^2 = d^2 $$

$$ 12544 + 4356 = d^2 $$

$$ 16900 = d^2 $$

$$ d = 130 $$

Step 10: Solve triangle j.

$$ 35^2 + 12^2 = a^2 $$

$$ 1225 + 144 = a^2 $$

$$ 1369 = a^2 $$

$$ a = 37 $$

Step 11: Solve triangle k.

$$ e^2 + 3^2 = 5^2 $$

$$ e^2 + 9 = 25 $$

$$ e^2 = 16 $$

$$ e = 4 $$

Step 12: Solve triangle l.

$$ 10^2 + z^2 = 26^2 $$

$$ 100 + z^2 = 676 $$

$$ z^2 = 576 $$

$$ z = 24 $$

Answer:

• a. \( a = 13 \)
• b. \( c = 20 \)
• c. \( x = 10 \)
• d. \( b = 7 \)
• e. \( s = 17 \)
• f. \( w = 15 \)
• g. \( k = 16 \)
• h. \( y = 178 \)
• i. \( d = 130 \)
• j. \( a = 37 \)
• k. \( e = 4 \)
• l. \( z = 24 \)