Slide 1 7-7 Home Maintenance and Improvement-1 - PowerPoint Presentation

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7-7Home Maintenance and Improvement-1

OBJECTIVES

Find missing sides of right triangles using the Pythagorean theorem.

Use the converse of the Pythagorean theorem.

Find the slope of a line.

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7-7Home Maintenance and Improvement-2

OBJECTIVES

Describe proportions in similar triangles.

Find missing sides of right triangles using trigonometry.

Find missing angles in right triangles using inverse trigonometric functions.

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Slide 3 Key Termstrigonometry

legshypoteneusepitchrise

runsimilarproportionmeansextremesangle of elevationtangent

sine

cosine

Inverse trigonometric functions

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How do you maintain your home and your property?

Think about the items around a house that need upkeep. What might it cost to pay for repairs and improvements?How can you budget for this?

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Example 1

Ana is planning to build a 15-foot by 20-foot rectangular deck off of the rear of her house. She is going to put stakes at the corners of the plot and lay string from stake to stake. She wants to make sure she has a perfect right angle to start. How can she do this?

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Example 1Ana is planning to build a 15-foot by 20-foot rectangular deck off of the rear of her house. She is going to put stakes at the corners of the plot and lay string from stake to stake. She wants to make sure she has a perfect right angle to start. How can she do this?

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Example 2

Manny is hiring a roofer to do some work on his house. The steepness of the roof will affect the labor cost he is charged. Below is a side view of Manny’s roof. How can he mathematically describe the steepness?

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Example 2

Manny is hiring a roofer to do some work on his house. The steepness of the roof will affect the labor cost he is charged. Below is a side view of Manny’s roof. How can he mathematically describe the steepness?

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Example 3Noah has a tree in his backyard that he wants to make sure cannot fall on his house if there is a bad storm. The tree is 52 feet from his house. In a picture he took, the tree is 5.5 x 6.2 inches. How can he find the height of the tree?

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Example 3Noah has a tree in his backyard that he wants to make sure cannot fall on his house if there is a bad storm. The tree is 52 feet from his house. In a picture he took, the tree is 5.5 x 6.2 inches. How can he find the height of the tree?

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Example 3Noah has a tree in his backyard that he wants to make sure cannot fall on his house if there is a bad storm. The tree is 52 feet from his house. In a picture he took, the tree is 5.5 x 6.2 inches. How can he find the height of the tree?

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Example 3Noah has a tree in his backyard that he wants to make sure cannot fall on his house if there is a bad storm. The tree is 52 feet from his house. In a picture he took, the tree is 5.5 x 6.2 inches. How can he find the height of the tree?

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Example 4

Jessica is purchasing a ladder so she can save money and clean her own gutters. She needs to find the height of her two-story house to make sure she buys a ladder long enough. Below is a diagram of her house. How high are the gutters?

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Example 4

Jessica is purchasing a ladder so she can save money and clean her own gutters. She needs to find the height of her two-story house to make sure she buys a ladder long enough. Below is a diagram of her house. How high are the gutters?

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Example 4

Jessica is purchasing a ladder so she can save money and clean her own gutters. She needs to find the height of her two-story house to make sure she buys a ladder long enough. Below is a diagram of her house. How high are the gutters?

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Example 4

Jessica is purchasing a ladder so she can save money and clean her own gutters. She needs to find the height of her two-story house to make sure she buys a ladder long enough. Below is a diagram of her house. How high are the gutters?

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Example 5

Nabil completed Reality Check project 5 and built a clinometer. He wants to find the height of a tree that is on level ground in his backyard. He uses a tape measure and his clinometer to create the following diagrams. How high is the tree?

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Example 5

Nabil completed Reality Check project 5 and built a clinometer. He wants to find the height of a tree that is on level ground in his backyard. He uses a tape measure and his clinometer to create the following diagrams. How high is the tree?

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Example 5

Nabil completed Reality Check project 5 and built a clinometer. He wants to find the height of a tree that is on level ground in his backyard. He uses a tape measure and his clinometer to create the following diagrams. How high is the tree?

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Example 6

The Americans with Disabilities Act (ADA) states that ramps for wheelchairs should have a slope of 1/12 or less. What does the angle of elevation of a ramp have to be to get ADA approval?

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Example 6

The Americans with Disabilities Act (ADA) states that ramps for wheelchairs should have a slope of 1/12 or less. What does the angle of elevation of a ramp have to be to get ADA approval?

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Example 6

The Americans with Disabilities Act (ADA) states that ramps for wheelchairs should have a slope of 1/12 or less. What does the angle of elevation of a ramp have to be to get ADA approval?

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Example 6

The Americans with Disabilities Act (ADA) states that ramps for wheelchairs should have a slope of 1/12 or less. What does the angle of elevation of a ramp have to be to get ADA approval?