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? points a, b are marked on either side of ceiling line on top. point c below ceiling line with extended point as lamp is joined by a line. a and b make 50 degrees and 70 degrees with ac and bc measuring 43 and 35 centimeters. ab marked question mark. a. 25.0 centimeters b. 38.3 centimeters c. 39.6 centimeters d. 42.4 centimeters

Answer 1

To find the distance between the points of suspension on the ceiling, we can use the Law of Cosines.

Step-by-step explanation:

To find the distance between the points of suspension on the ceiling, we can use the Law of Cosines. Let's label the points of suspension as A and B. The given lengths of the strings are AB = 43 cm and AC = 35 cm. The angles CAB and CBA are 50° and 70° respectively. To find the distance AB, we can use the formula:

AB = sqrt(AC^2 + BC^2 - 2 * AC * BC * cos(180° - CAB - CBA))

Substituting the given values, we get:

AB = sqrt((35 cm)^2 + (43 cm)^2 - 2 * (35 cm) * (43 cm) * cos(60°))

Calculating this gives us AB ≈ 42.4 cm. Therefore, the correct answer is (d) 42.4 centimeters.