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IM Geo.4.1 Lesson: Angles and Steepness

Triangle is similar to triangle . Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

Find the values of . If there is not enough information, what else do you need to know?

Find the values of . If there is not enough information, what else do you need to know?

Find the values of . If there is not enough information, what else do you need to know?

Some buildings offer ramps in addition to stairs so people in wheelchairs have access to the building. What characteristics make a ramp safe?

A school has 4 steps to the front door. Each step is 7 inches tall. Design a ramp for the school.

Here is the Americans with Disabilities Act (ADA) guidelines.

Americans with Disabilities Act Ramp Guidelines

Ramps are required for any change in level greater than inch. Ramps have a maximum slope of 1:12 (4.8 degrees) Ramps have a minimum width of 36 inches. There must be a minimum 5 feet by 5 feet flat area at the top and bottom of the ramp for turning. Ramps may be no longer than 30 feet horizontally between flat rest or turn platforms.

Does your design follow the rules of this law? If not, draw a new design that does.

A ramp with a length to height ratio of  forms a right triangle with a 4.8 degree angle. What is the angle measurement if the base is only 6 units long and the height is 1 unit tall?

When the length is half as long does that make the angle half as big?

What is the angle measurement if the base is 6 units long and the height is increased to 2 units tall?

When the height is twice as tall does that make the angle twice as big?