The length of the side BC is 3 units.
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,
The right triangle is shown in the figure.
Let the distance BC be x and
The side AB be y.
According to trigonometric ratios,
[tex]tan \theta=\frac{opposite}{adjacent}[/tex]
Consider Δ ABD,
⇒ [tex]tan (20) = \frac{y}{x+15}[/tex]
⇒ [tex]0.3639=\frac{y}{x+15}[/tex]
⇒ [tex]y=0.3639(x+15)[/tex] -------- (1)
Now consider Δ ABC,
⇒ [tex]tan(65)=\frac{y}{x}[/tex]
⇒ [tex]2.144=\frac{y}{x}[/tex]
⇒ [tex]y=2.144x[/tex] --------- (2)
From equation 1 and 2,
⇒ [tex]2.144x=0.3639(x+15)[/tex]
⇒ [tex]2.144x=0.3639x+5.4585[/tex]
⇒ [tex]1.7801x=5.4585[/tex]
⇒ [tex]x=\frac{5.4585}{1.7801}[/tex]
⇒ [tex]x=3.06[/tex] ≈ [tex]3[/tex]
Hence we can conclude that the length of the side BC is 3 units.
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