Minggu, 11 Maret 2012

PYTHAGOREAN THEOREM IN DAILY LIFE

Good morning all, my name is Nanda Putri Amalia from the International class of Mathematics Education.

Let me explain to you about the Pythagorean Theorem in daily life.

Open the Marsigits book page 153, look at the exercise.

  1. The recommended distance to watch the television is 6 times of the length of the diagonal of the television. Determine the exact distance to watch a 20 inch television!

Answer:

We know that the 1 inch television means that the length of the diagonal of the television is 1 inch or 2. 54 cm .

The 20 inch television means that the diagonal is 20 times 2 .54 is 50. 8 cm.

So, the recommended distance to watch a 20 television is 50. 8 times 6 is equal 3098 cm.

2. Amron and Cathy are playing a kite. The length of the string is 50 m. Cathy is standing below the kite and making a 30 m distance with Amron. Determine the exact height of the kite!

Answer:

We assume that the length of the string as the hypotenuse (c), the distance between Cathy and Amron as the base of triangle (a) and the hight of the kite as the upright side of triangle (b). So, we can use the phytagorean theorem.

a = 30 m

c = 50 m

b = ...?

c2 = a2 + b2

we exchange the position of b,

c2 - b2= a2

502 – 302 = a2

2500 – 900 = a2

the root of 1600 = a

a = 40 m

so, the exact high of the kite is 40 m.

3. Joni is swimming across a river of 12 meters width. Just before he is reaching the opposite of the river, an unexpected wave is taking Joni further as far 5 meters. Determine the distance between the first place and his place now!

Answer:

We assume that 12 meters as the upright side of triangle and 5 meters as the base of triangle.

hypotenuse = the root of = the root of = the root of 169 = 13 meters

so, the distance between the first place and his place now is 13 meters.

4. A 4 meter steel bar is leaning on a vertical wall and making 60° angle with ground.

a. Determine the exact distance of A and C!

b. Determine the exact distance of B and C!

Answer:

To solve this problem, we have to know about the ratio of lengths of sides of a right triangle that has 60° angle. The ratio of the lengths of a right ABC triangle with c as the hypotenuse and has 60° angle is a : b : c = 1 : the root of 3: 2.


We was know the ratio. Now, we use the comparison to know the exact distance that we're looking for.


a. b/the root of 3= c/2

b = [(the root of 3) times 4] divided by 2

b = 2 times the root of 3

b. a/1= c/2

a = (4 . 1) divided by 2

a = 2


so, the exact distance of A and C (b) is 2 times the root of 3 m and the exact distance of B and C (a) is 2 m.

5. A triangle is made by three bars of steel. The lengths of two bars are 20 cm and 48 cm.

a. Determine the length of the third bar thus forming right triangle!

b. If the length of the third bar is less than 48 cm, what kind of triangle formed?

c. If the length of th third bar is more than 52 cm, what kind of triangle formed?

Answer:

a. If we want to form the right triangle (c as the hypotenuse), so we use the theorem:

"If c2 = a2 + b2, then ΔABC is a right triangle"

so, the length of the third bar to form the right triangle is:

c2 = 202 + 482

c2 = 400 + 2304

c = the root of 2704

c = 52 cm

b. If the length of the third bar is less than 48 cm (c as the hypotenuse), we use the theorem:

"If c2 < a2 + b2, then ΔABC is an acute triangle"

c2 < 482 + 202

c < the root of 2704

c < 52 cm

based on the theorem above, if the length of the hypotenuse is less than 48 cm, the kind of triangle formed is acute triangle.

c. If the length of the third bar is more than 55 cm (c as the hypotenuse), we use the theorem:

"If c2 > a2 + b2, then ΔABC is an obtuse triangle."

so, the length of the third bar is:

c2 > 482 + 202

c > the root of 2704

c > 52 cm

based on the theorem above, if the length of the hypotenuse is more than 55 cm, the kind of triangle formed is obtuse triangle.

Ok friends, I hope that you have understand about the Pythagorean theorem in daily life.

Thank you for your attention.

Wassalamu'alaykum wr.wb.

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