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]);
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.