Question

name: levi.h. class: topic: date: main ideas/questions notes parts of a right triangle
a b c - sides a and b are called ____ - side c is called the ____ what is the pythagorean theorem? the pythagorean theorem is used to find a missing side length on a ______ triangle! formula: practice! find the missing side of each triangle. round to the nearest tenth. 1.
8 in 7 in x 2.
18 ft 15 ft x 3.
6 cm 13 cm x 4.
30 yd 25 yd x 5.
12 in 20 in x 6.
49 m 44 m x

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). We will use this formula to find the missing side \(x\) in each right triangle.

Step2: Solve Problem 1

For the first triangle, the legs are \(a = 7\) in and \(b=8\) in, and \(x\) is the hypotenuse.
Using the formula \(x^{2}=7^{2}+8^{2}\)
\(x^{2}=49 + 64=113\)
\(x=\sqrt{113}\approx10.6\) in (rounded to the nearest tenth)

Step3: Solve Problem 2

For the second triangle, the legs are \(a = 15\) ft and \(b = 18\) ft, and \(x\) is the hypotenuse.
Using the formula \(x^{2}=15^{2}+18^{2}\)
\(x^{2}=225+324 = 549\)
\(x=\sqrt{549}\approx23.4\) ft (rounded to the nearest tenth)

Step4: Solve Problem 3

For the third triangle, one leg \(a = 6\) cm, hypotenuse \(c = 13\) cm, and \(x\) is the other leg.
Using the formula \(x^{2}=c^{2}-a^{2}\)
\(x^{2}=13^{2}-6^{2}=169 - 36=133\)
\(x=\sqrt{133}\approx11.5\) cm (rounded to the nearest tenth)

Step5: Solve Problem 4

For the fourth triangle, legs \(a = 25\) yd and \(b = 30\) yd, and \(x\) is the hypotenuse.
Using the formula \(x^{2}=25^{2}+30^{2}\)
\(x^{2}=625 + 900=1525\)
\(x=\sqrt{1525}\approx39.0\) yd (rounded to the nearest tenth)

Step6: Solve Problem 5

For the fifth triangle, one leg \(a = 12\) in, hypotenuse \(c = 20\) in, and \(x\) is the other leg.
Using the formula \(x^{2}=c^{2}-a^{2}\)
\(x^{2}=20^{2}-12^{2}=400 - 144 = 256\)
\(x=\sqrt{256}=16\) in

Step7: Solve Problem 6

For the sixth triangle, one leg \(b = 44\) m, hypotenuse \(c = 49\) m, and \(x\) is the other leg.
Using the formula \(x^{2}=c^{2}-b^{2}\)
\(x^{2}=49^{2}-44^{2}=2401-1936 = 465\)
\(x=\sqrt{465}\approx21.6\) m (rounded to the nearest tenth)

Answer:

1. \(x\approx10.6\) in
2. \(x\approx23.4\) ft
3. \(x\approx11.5\) cm
4. \(x\approx39.0\) yd
5. \(x = 16\) in
6. \(x\approx21.6\) m