For the next three questions, choose which is the most appropriate method to solve the problem, explain your answer.
a) SOACAHTOA
b) The Sine Law
c) The Cosine Law
d) The problem cannot be solved without further information
1) Yachts in a race have to sail a triangular course. First they sale in a direction of 135 deg (clockwise from North) for 8km. They change direction and sail on a course of 045 deg (clockwise from north) The last part of the course is to return by sailing due West. How far was the second part of the course? ... The most appropriate method for solving this problem is:
2) In Triangle ABC, BA= 9cm, AC= 13cm, and <ABC= 113 deg. Calculate the measure of <BCA ... The most appropriate method for solving this problem is:
3) A pilot leaves base flying on a bearing of 340 deg. After 30 minutes he changes course to 108 deg and flies in this direction until he is due north of base. How far does he have to fly South to return to base? ... The most appropriate method for solving this problem is:
1) The most appropriate method for solving this problem is the cosine law (c). The problem requires finding the distance of the second leg in a triangular course. The cosine law can be used to solve for the length of the side when the measures of two angles and the included side are known.
2) The most appropriate method for solving this problem is the sine law (b). The problem involves finding the measure of an angle in a triangle when the lengths of the sides and another angle are known. The sine law relates the ratios of the lengths of the sides to the sines of the opposite angles.
3) The most appropriate method for solving this problem is SOHCAHTOA (a). The problem involves finding the distance the pilot needs to fly in a specific direction. SOHCAHTOA is a trigonometric method that relates the ratios of the lengths of the sides of a right-angled triangle to the sine, cosine, and tangent of its angles.
1) The most appropriate method for solving this problem is: c) The Cosine Law
The problem provides information about the lengths of two sides of the triangular course and the included angle. The Cosine Law is best suited for solving problems involving triangles where you have information about the lengths of two sides and the included angle.
2) The most appropriate method for solving this problem is: a) SOACAHTOA
The problem provides information about the lengths of two sides of a triangle and the angle between them. SOH-CAH-TOA is a mnemonic device used to remember the ratios of sides in a right triangle. Given the sides BA and AC, we have enough information to use trigonometric ratios to find the measure of angle BCA.
3) The most appropriate method for solving this problem is: d) The problem cannot be solved without further information
The problem provides information about the pilot's initial bearing, the change in course, and the duration of the flight. However, there is no information given about the speed of the pilot or the distance covered during each segment of the flight. Without this additional information, it is not possible to determine how far the pilot has to fly South to return to the base.