Given:
In a right angle triangle ABC, [tex]\angle B=90^\circ,x=8.7\ m[/tex], and [tex]\theta = 45^\circ[/tex]
To find:
The value of AC.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos \theta =\dfrac{BC}{AC}[/tex]
[tex]\cos (45^\circ) =\dfrac{8.7}{AC}[/tex]
[tex]\dfrac{1}{\sqrt{2}}=\dfrac{8.7}{AC}[/tex]
On cross multiplication, we get
[tex]AC=8.7\times \sqrt{2}[/tex]
[tex]AC=12.30365799[/tex]
[tex]AC\approx 12.304[/tex]
Therefore, the measure of AC is 12.304 m.
