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valina [46]
3 years ago
8

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

e side adjacent to angle C

Mathematics
2 answers:
IrinaVladis [17]3 years ago
6 0

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)
 
11111nata11111 [884]3 years ago
4 0

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}}  .

Learn more:  

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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.

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