The approximate length of the side adjacent to angle [tex]C[/tex] is [tex]\boxed{{\mathbf{7}}.7{\mathbf{ inches}}}[/tex] .
Further explanation:
The trigonometry ratio used in the right angle triangles.
The cosine ratio can be written as,
[tex]\cos \theta = \dfrac{length\ of\ the\ side\ adjacent\ to\ \theta }{hypotenuse}[/tex]
Here, base is the length of the side adjacent to angle [tex]\theta[/tex] and hypotenuse is the longest side of the right angle triangle where the length of side opposite to angle [tex]\theta[/tex] is perpendicular that is used in the sine ratio.
Step by step explanation:
Step 1:
The attached right angle triangle can be observed from the given information.
First define the hypotenuse and the base of the triangle.
The side [tex]BC[/tex] is adjacent to angle [tex]C[/tex] and the side [tex]AC[/tex] is the hypotenuse of [tex]\Delta ABC[/tex] .
Therefore, the [tex]{\text{length of the side adjacent to C}}=BC[/tex] and [tex]{\text{hypotenuse}}=10[/tex] .
Step 2:
Since, the cosine ratio is [tex]\cos \theta = \dfrac{length\ of\ the\ side\ adjacent\ to\ \theta }{hypotenuse}[/tex]
Now put the value [tex]{\text{length of the side adjacent to C}}=BC[/tex] and [tex]{\text{hypotenuse}}=10[/tex] in the cosine ratio.
[tex]\begin{aligned}\cos C&=\frac{{BC}}{{10}}\\{\text{co}}s40&=\frac{{BC}}{{10}}\\0.766&=\frac{{BC}}{{10}}\\BC&=7.66\\\end{aligned}[/tex]
Therefore, the approximate length of the side adjacent to angle [tex]C[/tex] is [tex]7.66{\text{ inches}}[/tex] .
Learn more:
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Trigonometry
Keywords: Distance, Pythagoras theorem, base, perpendicular, hypotenuse, right angle triangle, units, squares, sum, cosine ratio, adjacent side to angle, opposite side to angle.
