randRange(0, 359) randRange(20, 70)

Is the shown angle acute, right, or obtuse?

var ANGLE_TWO = ANGLE_ONE + DIFF; var ANGLE_ONE_R = ANGLE_ONE * PI / 180; var ANGLE_TWO_R = ANGLE_TWO * PI / 180; init({ range: [ [-11, 31], [-10, 10] ], scale: 20 }); path([ [5 * cos( ANGLE_ONE_R ), 5 * sin( ANGLE_ONE_R )], [0, 0], [5 * cos( ANGLE_TWO_R ), 5 * sin( ANGLE_TWO_R )] ]); DIFF == 90 ? path([ [1 * cos( ANGLE_ONE_R ), 1 * sin( ANGLE_ONE_R )], [sqrt(2) * cos( ANGLE_ONE_R + PI / 4 ), sqrt(2) * sin( ANGLE_ONE_R + PI / 4)], [1 * cos( ANGLE_TWO_R ), 1 * sin( ANGLE_TWO_R )] ]) : arc( [0,0], 1, ANGLE_ONE, ANGLE_TWO ); addMouseLayer(); graph.protractor = new Protractor( [14, -8] );
Acute
  • Acute
  • Right
  • Obtuse
graph.protractor.moveTo( 0, 0 ); graph.protractor.rotateTo( 360 - ANGLE_ONE ); label( [ 9 * cos( toRadians( ANGLE_ONE + DIFF ) ), 9 * sin( toRadians( ANGLE_ONE + DIFF ) ) ], "\\color{" + PINK + "}{" + DIFF + "^{\\circ}}" );

The shown angle measures less than 90^\circ.

label( [ 9 * cos( toRadians( ANGLE_ONE + DIFF ) ), 9 * sin( toRadians( ANGLE_ONE + DIFF ) ) ], "\\color{" + PINK + "}{" + DIFF + "^{\\circ}}" );

Therefore, it is an acute angle.

randRange(110, 160)
Obtuse
graph.protractor.moveTo( 0, 0 ); graph.protractor.rotateTo( 360 - ANGLE_ONE );

The shown angle measures more than 90^\circ.

label( [ 9 * cos( toRadians( ANGLE_ONE + DIFF ) ), 9 * sin( toRadians( ANGLE_ONE + DIFF ) ) ], "\\color{" + PINK + "}{" + DIFF + "^{\\circ}}" );

Therefore, it is an obtuse angle.