Question

In a right triangle, angle C measures 40. the hypotenuse of the triangle is 10 inches long. what is the approximate length of the side adjacent to angle C

Answer 1

Since angle C is not 90 degrees, it's one of the acute angles
in the right triangle.


               (The side adjacent to angle C ) divided by (hypotenuse)

is the cosine of angle C .       


                    (adjacent) / (10 inches)  =  cos(40 degrees)

Multiply each side by (10 inches):

                    Adjacent side = (10 inches) x cos(40) =

                                              (10 inches)  x  0.766  = 

                                                              7.66 inches   (rounded)
 

Answer 2

The approximate length of the side adjacent to angle $C$  is $\boxed{{\mathbf{7}}.7{\mathbf{ inches}}}$ .

Further explanation:

The trigonometry ratio used in the right angle triangles.

The cosine ratio can be written as,

  $\cos \theta = \dfrac{length\ of\ the\ side\ adjacent\ to\ \theta }{hypotenuse}$

Here, base is the length of the side adjacent to angle $\theta$  and hypotenuse is the longest side of the right angle triangle where the length of side opposite to angle $\theta$  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 $BC$  is adjacent to angle $C$  and the side $AC$  is the hypotenuse of $\Delta ABC$ .

Therefore, the ${\text{length of the side adjacent to C}}=BC$  and ${\text{hypotenuse}}=10$ .

Step 2:

Since, the cosine ratio is $\cos \theta = \dfrac{length\ of\ the\ side\ adjacent\ to\ \theta }{hypotenuse}$  

Now put the value ${\text{length of the side adjacent to C}}=BC$  and  ${\text{hypotenuse}}=10$ in the cosine ratio.

$\begin{aligned}\cos C&=\frac{{BC}}{{10}}\\{\text{co}}s40&=\frac{{BC}}{{10}}\\0.766&=\frac{{BC}}{{10}}\\BC&=7.66\\\end{aligned}$

Therefore, the approximate length of the side adjacent to angle $C$  is $7.66{\text{ inches}}$  .

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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.