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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

Respuesta :

pingwin09
The answer is 39.6 centimeters.
This can be done by using cosine law.

Answer: Third option is correct.

Step-by-step 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,

[tex]\cos 50\textdegree=\frac{BC}{AC}\\\\\cos 50\textdegree=\frac{BC}{43}\\\\BC=\cos 50\textdegree\times 43\\\\BC=27.63[/tex]

Similarly,

In ΔPCR,

[tex]\cos 70\textdegree=\frac{CR}{PR}\\\\\cos 70\textdegree=\frac{CR}{35}\\\\CR=\cos 50\textdegree\times 35\\\\CR=11.97[/tex]

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

[tex]BC+CR=11.97\ cm+27.63\ cm\\\\=39.6\ cm[/tex]

Hence, third option is correct.


Ver imagen RenatoMattice

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