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Some Geometry help please?
I am confused with these questions? I need a little help.
1. The ratio of the angle measures of a pentagon is 4:5:3:8:7. What is the measure of the smallest angle?
2. Three sides of a triangle measure 0.5, 0.6, and 0.8. Two sides of a similar triangle measure 2 and 3.2. What is the length of the third side?
3. An eiffel tower mural is 2 meters high and 0.77 meters wide. If the actual tower is 125 meters wide, how tall is it to the nearest meter?
4. Rob is making for his young son a replica armchair of the one he uses. The ratio of the length of the arm of the old chair to that of the new chair is 3:2. The arm of the old chair is 9 inches long. How many inches long will the arm of the new chair be?
Thank you !
1.)Add up all the numbers in the ratio. 4+5+3+8+7=27. Now find the total measure of the interior angles.
Use the following formula: (number of sides in polygon - 2) * 180. 5-2=3*180=540. Divide the total number of degrees by the total ratio . 540/27=20. The smallest angle is "3", so 20*3=60. Check your work by multiplying all the numbers by 20 and then add them up to see if the equal 540.
2.) The two triangle have similar shape, but do not have the same exact length. This means there is a scale factor between the two. Compare the numbers 0.5 and 2. The first side of triangle 1 is 4 times less than the first side of triangle 2. Same goes for the numbers 0.8 and 3.2. Multiply 4 by 0.6= 2.4 for the third side of triangle 2.
3.)125/0.77=Approximately 63 meters.
4.)3:2. Multiply each side by 3. 3*3=9, 3*2=6. The arm of the new chair will be 6 inches long.
The Eiffel Chair, Charles and Ray Eames