Mathematics, 19.09.2019 01:00 ericamoody14

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?
6.4 inches
7.7 inches
8.4 inches
13.1 inches

Answers: 2

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Answers

Answer from: penny3109

The correct option is Option C $\boxed{{\mathbf{7}}{\mathbf{.66 inches}}}$ .

Further explanation:

The cosine ratio can be represented as,

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

Here, base is the length of the side adjacent to angle $\theta$ and hypotenuse is 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:

From the given information, the observed right angle is attached.

First find the hypotenuse and the base of the right angle triangle.

It can be seen from the attached figure that the side is adjacent to angle and the side is the hypotenuse of triangle.

Thus, the ${\text{base}}=BC$ and ${\text{hypotenuse}}=10$ .

Step 2:

We know that the cosine ratio is $\cos \theta =\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}$ .

Therefore, it can be written as,

$\cos \theta=\frac{{BC}}{{AC}}$

Now substitute the value BC=x and ${\text{AC}}=10$ in the cosine ratio.

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

Therefore, the approximate length of the side adjacent to angle is $7.7{\text{ inches}}$ .

Thus, option C is correct.

Learn more:

Learn more about the distance between two points on the number line link Learn more about the distance between two coordinates of the line link Learn more about what is the domain of the function on the graph? all real numbers all real numbers greater than or equal to 0 all real numbers greater than or equal to –2 all real numbers greater than or equal to –3 link

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.

In a right triangle, angle c measures 40°. the hypotenuse of the triangle is 10 inches long. what is

Answer from: anitadefrances

Answer

Find out the what is the approximate length of the side adjacent to angle C .

To prove

As given

In a right triangle, angle C measures 40°.

The hypotenuse of the triangle is 10 inches long.

Than by using the trignometric identity

$cos\angle C= \frac{Base}{Hypotenuse}\\cos\angle C= \frac{BC}{AC}$

As shown the diagram is given below

AC= 10 inches , ∠C = 40 °

cos 40 = 0.766 (approx)

Put in the above formula

0.766 × 10 = BC

7.66 = BC

7.7 inches (approx) = BC

Option (b) is correct .

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

Hello! i hope this
since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.