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

Is the shown angle acute, right, or obtuse?

var ANGLE_TWO = ANGLE_ONE + DIFF; var ANGLE_ONE_R = toRadians(ANGLE_ONE); var ANGLE_TWO_R = toRadians(ANGLE_TWO); angle.COS1 = cos(ANGLE_ONE_R); angle.SIN1 = sin(ANGLE_ONE_R); angle.COS2 = cos(ANGLE_TWO_R); angle.SIN2 = sin(ANGLE_TWO_R); init({ range: [ [-11, 31], [-10, 10] ], scale: 20 }); line([0, 0], [5 * angle.COS1, 5 * angle.SIN1], { arrows: "->"}); line([0, 0], [5 * angle.COS2, 5 * angle.SIN2], { arrows: "->"}); if (DIFF === 90) { path([[angle.COS1, angle.SIN1], [sqrt(2) * cos(ANGLE_ONE_R + PI / 4), sqrt(2) * sin(ANGLE_ONE_R + PI / 4)], [angle.COS2, angle.SIN2]]); } else { arc([0, 0], 1, ANGLE_ONE, ANGLE_TWO); } addMouseLayer(); graph.protractor = protractor([14, -8]);
Acute

- Acute
- Right
- Obtuse

graph.protractor.moveTo( 0, 0 ); graph.protractor.rotateTo( 540 - ANGLE_ONE - DIFF );

The shown angle measures less than `90^\circ`.

label([9 * angle.COS1, 9 * angle.SIN1], "\\color{" + PINK + "}{" + DIFF + "^{\\circ}}");

Therefore, it is an acute angle.

90
Right
graph.protractor.moveTo( 0, 0 ); graph.protractor.rotateTo( 540 - ANGLE_ONE - DIFF );

The shown angle measures `90^\circ`.

label([9 * angle.COS1, 9 * angle.SIN1], "\\color{" + PINK + "}{" + DIFF + "^{\\circ}}");

Therefore, it is a right angle.

randRange(110, 160)
Obtuse
graph.protractor.moveTo( 0, 0 ); graph.protractor.rotateTo( 540 - ANGLE_ONE - DIFF );

The shown angle measures more than `90^\circ`.

label([9 * angle.COS1, 9 * angle.SIN1], "\\color{" + PINK + "}{" + DIFF + "^{\\circ}}");

Therefore, it is an obtuse angle.