Question

Please help me with geometry

Answer 1

If angle B is the reference angle, in our triangle we are given the measures of the sides opposite the angle and the hypotenuse of the right triangle formed.  This is the sin ratio that uses the side opposite the angle and the hypotenuse.  So to find the measure of angle B, we would use the inverse sin of 21/42. That's the first one.  The second one asks for the sin and cos of the acute angles in the triangle.  Angles A and B are the acute angles.  Looking at angle A first, the side across from it has a measure of 55, and the hypotenuse has a measure of 73, so the sin of angle A is 55/73.  The cos of an angle uses the side adjacent to the acute angle and the hypotenuse.  That means that the cos of angle A is 48/73.  Looking at angle B now, the side across from angle B is 48 and the hypotenuse is 73, so sin B = 48/73. Cos of B is side adjacent over hypotenuse, so cos B = 55/73.  Last choice is your answer.  As for the last question, the cosecant of an angle is the co-identity of the sin of the angle.  So we find the sin of the angle in ratio form and flip the fraction upside down.  The sin of theta in the triangle above is 7/25, so the csc of theta is 25/7, choice four above.