Respuesta :
Answer: 131.7 ft
Step-by-step explanation: use 148 as side measure b, then solve for measure of side a
with two given angles and one given side, use law of sines.
a = b•sin(A)/sin(B) = 131.71071
c = b•sin(C)/sin(B) = 166.89278
if you want to find angle measures:
180-A-B
180-49-58=73
C=73
The length of the string attached to stake B is 166.3 feet.
What is trigonometry?
Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
An angle of elevation of stake A = 49°
The length of the string attached to stake A,a = 148 feet
An angle of elevation of stake B = 58°
Let the length of the string attached to stake B be b.
Then by law of sines,
[tex]\frac{Sine A}{a}=\frac{Sine B}{b}[/tex]
On substituting the above values,
⇒ [tex]\frac{Sine 49}{148}=\frac{Sine 58}{b}[/tex]
⇒ [tex]b=\frac{(Sine 58)(148)}{Sine49}[/tex]
⇒ [tex]b=\frac{(0.8480)(148)}{0.7547}[/tex]
⇒ [tex]b=166.29[/tex] ≈ [tex]166.3[/tex]
Hence we can conclude that the length of the string attached to stake B is 166.3 feet.
Learn more about trigonometry here
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