"How did you program your robot to move in a perfect triangle?" Arianna asks, sounding impressed. "It always comes back to exactly where it started!" "My code uses the law of cosines and the law of sines." Raphael proudly replies. "For example, if it moves 3 m3\text{ m}3 m, turns 120?120^\circ120?, then moves 4 m4\text{ m}4 m more, it can compute the distance back to where it started as well as the angle it must turn." In Raphael's example, what distance would his robot compute? Do not round during your calculations. Round your final answer to the nearest hundredth of a meter

The distance computed is 6.08 m

Step-by-step explanation:

One of the sides (a) of the triangle has a length of 3 m, the other side (b) has a length of 4 m, and the angle (C) form between them measures 120°. The law of cosine states:

c² = a² + b² - 2ab cos C

Replacing with data (dimensions are omitted):

c² = 3² + 4² - 2(3)(4) cos 120°

c = √37

c = 6.08 m

the correct answer is 5 6 and 7

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: