Question

1. The scale drawing below is the base of an office building. The sale of the drawing is 1 unit : 6 feet. Redraw the scale drawing using a scale of 1 unit : 4 yard. Use the grid above.
2. A triangle has angles measuring 30 degrees and 90 degrees. The length of the included side is 6 cm. Tell whether the conditions form a unique triangle, more than one triangle, or no triangle.

Can someone answer these two questions for me quickly! Thank you so much!!!

Answer 1

11)

keeping in mind that, there are 3 feet in 1 yard, therefore, in 4 yards there are 4(3) feet or 12 feet.

now, 12 feet is twice as much as 6 feet.  If the original grid, had each unit length to be 6 feet, that means each square was a 6x6 square.  That means the new adjusted grid, will be twice as many feet per each unit, namely a 12 : 1.  Check the first picture below.

12)

check the second picture below, that's the 30-60-90 rule.

now, if one angle in the triangle is 30°, and another is 60°, the last one must be a 90° angle, so the triangle is a 30-60-90 triangle, and thus the 30-60-90 rule applies, with the ratios as you see in the picture.

so, if any of the sides has a value of 6, that will be a constraint to the other sides, since the other sides must be at a ratio of 6.

because of those ratios constraints, you can only make one unique triangle, if one side is 6, the others cannot fluctuate in length, they must be at a ratio of 6.