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:
you have ASA, so the final angle is easy to determine(it returned). I would use law of sines.
one the second, I would use law of sines.
this depends on his speed, which is not given.
1) The most appropriate method for solving this problem is the Cosine Law. The problem involves finding the distance of the second part of the course in a triangular race, given the initial and final directions and distances. The Cosine Law can be used to find the length of the side of a triangle when the lengths of the other two sides and the included angle are known. In this case, we have the lengths of the two sides (8km and unknown distance) and the included angle (90 degrees between the second part of the course and the West direction).
2) The most appropriate method for solving this problem is the Sine Law. The problem involves finding the measure of an angle in a triangle, given the lengths of two sides and the measure of the included angle. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all sides and angles of the triangle. In this case, we have two side lengths (9cm and 13cm) and the included angle (113 degrees).
3) The most appropriate method for solving this problem is SOH-CAH-TOA. The problem involves finding the distance the pilot needs to fly South to return to base, given initial and final bearings and flight times. SOH-CAH-TOA is a mnemonic acronym for three trigonometric ratios: Sine, Cosine, and Tangent, which relate the angles of a right triangle to the ratio of the lengths of its sides.
In this case, we know the initial bearing (340 degrees) and final bearing (108 degrees). We can use the Sine ratio (SOH) to find the distance the pilot flew North, and then subtract it from the initial distance to find the distance the pilot needs to fly South.