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

Answers

Answer 1

Answer:
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

Answer:

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,

$\cos \theta = (length\ of\ the\ side\ adjacent\ to\ \theta )/(hypotenuse)$

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 $\cos \theta = (length\ of\ the\ side\ adjacent\ to\ \theta )/(hypotenuse)$

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

$\begin{aligned}\cos C&=\frac{{BC}}{{10}}\n{\text{co}}s40&=\frac{{BC}}{{10}}\n0.766&=\frac{{BC}}{{10}}\nBC&=7.66\n\end{aligned}$

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.

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In ΔCDE, the measure of ∠E=90°, ED = 28, CE = 45, and DC = 53. What ratio represents the tangent of ∠C?

Answers

Answer:

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Answers

Answer:

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Answers

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