Question

The diagram illustrates a decorative lamp that is suspended from a ceiling by two strings. The first string is 43 centimeters long and makes a 50° angle with the horizontal. The second string is 35 centimeters long and makes a 70° angle with the horizontal. What is the distance between the points of suspension of the strings on the ceiling?

Answer 1

c = 39.61 centimeters

Explanation:

plato

Answer 2

From the given description above, we can conclude that the lamp suspended to the wall forms an oblique triangle. The first side measures 43 centimeters with an angle 50° to the horizontal and the other side measures 35 centimeters with 70° to the horizontal. We can use cosine law here to get the length of the other side.

c² = a² + b² - 2abcosC
c² = 43² + 35² - 2(43)(35)cos(180°-70°-50°)
c = 39.61 centimeters