Angles Examine the right triangles pictured below. Remember a right triangle has a 90° angle and that the sum of all of the angles in any triangle is equal to 180°. The two short sides of this right triangle have been labeled A and B. The longest side of a right triangle is known as the hypotenuse. The right angle is marked and the other two angles are marked with and that the right angle is opposite to the hypotenuse and that angle is opposite to side A and angle ‘a’ ‘b’. Notice ‘a’ ‘b’ is opposite to side B. Also, side B is adjacent (next to) side A. We use the Pythagorean Theorem to calculate the length of any side of a right triangle when the length of the other two sides is known. We use trigonometric relationships to calculate the length of any side of a right triangle when the length of one side and one angle is known. These relationships are easy to remember if you learn this a heap of The first letter of each word in silly phrase, “Oscar had apples”. the phrase helps you remember the sin, cos, tan relationships in that order. This is the same order as the buttons appear on a scientific calculator so that also simplifies the memory task! Using the right triangle above, solve for the following. Your calculator must be in degree mode. a. a = 55o and = 22 solve for and _______________ hypotenuse m, A B. b. a = 45o and = 15 solve for and _______________ A m/s, B hypotenuse. c. = 18.7 and a = 65o, solve for and _______________ B A hypotenuse. m d. = 9 and = 9 solve for a and _______________ A m B m, hypotenuse.
Angles Examine the right triangles pictured below. Remember a right triangle has a 90° angle and that the sum of all of the angles in any triangle is equal to 180°. The two short sides of this right triangle have been labeled A and B. The longest side of a right triangle is known as the hypotenuse. The right angle is marked and the other two angles are marked with ‘a’ and ‘b’. Notice that the right angle is opposite to the hypotenuse and that angle ‘a’ is opposite to side A and angle ‘b’ is opposite to side B. Also, side B is adjacent (next to) side A. We use the Pythagorean Theorem to calculate the length of any side of a right triangle when the length of the other two sides is known. We use trigonometric relationships to calculate the length of any side of a right triangle when the length of one side and one angle is known. These relationships are easy to remember if you learn this silly phrase, “Oscar had a heap of apples”. The first letter of each word in the phrase helps you remember the sin, cos, tan relationships in that order. This is the same order as the buttons appear on a scientific calculator so that also simplifies the memory task! Using the right triangle above, solve for the following. Your calculator must be in degree mode. a. a = 55o and hypotenuse = 22 m, solve for A and B. _______________ b. a = 45o and A = 15 m/s, solve for B and hypotenuse. _______________ c. B = 18.7 m and a = 65o, solve for A and hypotenuse. _______________ d. A = 9 m and B = 9 m, solve for a and hypotenuse. _______________