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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Length

Grade: 6-a Lesson: S3-L1

Explanation: Let us verify the answer here with the steps.

Description:

Step	Type	Explanation	Answer
1	Problem	Engineers are designing a suspension bridge with two main towers. The distance between the towers is 1,000 feet, and the height of each tower is 150 feet. What is the length of the suspension cable needed to connect the two towers?
2	Step	To find the length of a suspension cable between two towers in a suspension bridge, use the Pythagorean theorem.
3	Step	The cable forms a right triangle with the tower height and distance between them.
4	Step	In this case, the height of each tower is 150 feet, and the distance between the towers is 1,000 feet. Let’s call the length of the suspension cable "L".
5	Formula:	Using the Pythagorean theorem:	\$ L^2 = "(distance between the towers)"^2 + "(height of each tower)"^2 \$
6	Step	After substitution, we get	\$ L^2 = 1,000^2 + 150^2 \$
7	Step	After simplification, we get	\$ L^2 = 1,000,000 + 22,500 \$
8	Step	After addition, we get	\$ L^2 = 1,022,500\$
9	Step	Now, take the square root of both sides to find the length of the suspension cable:	\$ L = \sqrt(1,022,500) \$
10	Step	After simplification, we get	L = 1,011.23 feet
11	Step	So, the length of the suspension cable needed to connect the two towers is approximately 1,011.23 feet.
12		Answer	A

Step

Type

Explanation

Answer

Problem

Engineers are designing a suspension bridge with two main towers. The distance between the towers is 1,000 feet, and the height of each tower is 150 feet. What is the length of the suspension cable needed to connect the two towers?

Step

To find the length of a suspension cable between two towers in a suspension bridge, use the Pythagorean theorem.

Step

The cable forms a right triangle with the tower height and distance between them.

Step

In this case, the height of each tower is 150 feet, and the distance between the towers is 1,000 feet. Let’s call the length of the suspension cable "L".

Formula:

Using the Pythagorean theorem:

\$ L^2 = "(distance between the towers)"^2 + "(height of each tower)"^2 \$

Step

After substitution, we get

\$ L^2 = 1,000^2 + 150^2 \$

Step

After simplification, we get

\$ L^2 = 1,000,000 + 22,500 \$

Step

After addition, we get

\$ L^2 = 1,022,500\$

Step

Now, take the square root of both sides to find the length of the suspension cable:

\$ L = \sqrt(1,022,500) \$

Step

After simplification, we get

L = 1,011.23 feet

Step

So, the length of the suspension cable needed to connect the two towers is approximately 1,011.23 feet.

Answer