The lengths of the diagnoals of a rhombus are 16 cm and 30 cm. Find the perimeter and the measures of each of the angles of the rhombus.
PLEASE EXPLAIN!!!!
2007-04-11 14:59:25 · 5 answers · asked by 2 days after my B day :) 2 in Science & Mathematics ➔ Mathematics
The perimeter would be: 4*sqrt(8^2+15^2)=4*17=68.
The angles would be: 2*arctan(8/15) and 180-2arctan(8/15).
One would b 56.144 (approximately) and the other would be, angain approximate, 123.85 degrees.
2007-04-11 15:04:55 · answer #1 · answered by bruinfan 7 · 0⤊ 0⤋
This is a great question, I love rhombus questions like this! Thank you.
The diagonals of a rhombus do many things, two of which are bisect each other and they're perpendicular. So you have 4 congruent right triangles with side 8 and 15. Using Pythagorean theorem, you get the hypotenuse (which is the side of the rhombus) to be 17. Since the rhombus is equilaterial, its perimeter is 4*17 = 68 cm.
The diagonals also bisect the angles of the rhombus, so if you find the measures of each angle of these right triangles and double it, you will have the angles of the rhumbus. The angles in the triangles are arcsin (8/17) and arcsin (15/17). So the rhombus' angles are two times those angles, or 56.1° and 123.9°
2007-04-11 22:28:45 · answer #2 · answered by Kathleen K 7 · 0⤊ 0⤋
the diagonals perpindicularly bisect each other. you therefor have 8-15-17 right triangles so the sides are 17 cm & the perimeter=4s=4*17=68 cm
the acute angles is 2 arcsin 8/17=56°
THE OBTUSE ANGLE IS 180°-56°=124°
2007-04-11 22:13:32 · answer #3 · answered by yupchagee 7 · 0⤊ 0⤋
The perimeter is 16 * 2 + 30 * 2. i can't think of how you would find the angles. you probably have to trianguglate it though.
2007-04-11 22:09:31 · answer #4 · answered by Shamus O'Larry 4 · 0⤊ 0⤋
I love Questions about a Rhombus!!!!
2007-04-11 22:03:43 · answer #5 · answered by Chris M 2 · 0⤊ 1⤋