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

In a right triangle, we know that we have one angle that is 90 degrees. In order to calculate the length of the adjacent side we have to use the cosine function of angle C which will give us the adjacent side length. The cosine function is: adjacent/hypotenuse = cos (40). We know the hypotenuse length is 10, so the equation is now adjacent/10 = cos (40). Solving for adjacent length we get 7.66 inches.

Answer 2

The approximate length of the side adjacent to angle $C$  is $\boxed{{\mathbf{7}}{\mathbf{.66 inches}}}$ .

Further explanation:

The cosine ratio can be expressed as,

  $\cos\theta=\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}$

Here, base is the length of the side adjacent to angle $\theta$  and hypotenuse id the longest side of the right angle triangle.

The length of side opposite to angle $\theta$  is perpendicular that is used for the sine ratio.

Step by step explanation:

Step 1:

The observed right angle from the given information is attached.

First determine 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 ${\text{base}}=BC$  and ${\text{hypotenuse}}=10$ .

Step 2:

Since, the cosine ratio is $\cos\theta=\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}$ .

Now substitute the value ${\text{base}}=BC$  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.