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?

25.0 centimeters
38.3 centimeters
39.6 centimeters
42.4 centimeters

Answer 1

The answer is 39.6 centimeters.
This can be done by using cosine law.

Answer 2

Answer: Third option is correct.

Explanation:

since we have given that

Length of first string = 43 cm

Angle of elevation with the horizontal = 50°

Length of second string = 35 cm

Angle of elevation with the horizontal = 70°

We need to find the distance between the points of suspension of the strings on the ceiling .

WE will use "Cosine Law".

In ΔABC,

`\cos 50\textdegree=(BC)/(AC)\\\\\cos 50\textdegree=(BC)/(43)\\\\BC=\cos 50\textdegree* 43\\\\BC=27.63`

Similarly,

In ΔPCR,

`\cos 70\textdegree=(CR)/(PR)\\\\\cos 70\textdegree=(CR)/(35)\\\\CR=\cos 50\textdegree* 35\\\\CR=11.97`

So, Total distance between the points of suspension of the strings on the ceiling is given by

`BC+CR=11.97\ cm+27.63\ cm\\\\=39.6\ cm`

Hence, third option is correct.