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Ede4ka [16]
3 years ago
5

What is the length of bc ? Round to the nearest tenth.

Mathematics
2 answers:
enyata [817]3 years ago
4 0
Draw a line from 65 to the opposite side you get X and 16 is the hypotenuse
So this sine opposite over hypotenuse

Sin (65)= X/ 16
Sin (65) times 16 is 14.5
Ierofanga [76]3 years ago
4 0

The length BC is \boxed{14.5\:\text{cm}}.

Explanation:

The given triangle is a right angle triangle at angle C and the angle A equals 65^{\circ}.  

In a right angled triangle, the two sides which make the right angle or which are perpendicular, are called the base and the height of the right angle triangle. The third side, the largest of the three is called the hypotenuse of the right angled triangle.  

From the figure, it is observed that AC is the base, BC is the height and AB is the hypotenuse.

The formula for trigonometric identities \sin(\theta), \cos(\theta) and \tan(\theta), where \theta is the angle between hypotenuse and base, is as shown below.

\sin\theta =\dfrac{\text{Height}}{\text{Hypotenuse}}\\\cos\theta=\dfrac{\text{Base}}{\text{Hypotenuse}}\\\tan\theta=\dfrac{\text{Height}}{\text{Base}}

Substitute 65^{\circ} for \theta, 16 for hypotenuse and x for height in the formula for sine of angle \theta.

\boxed{\begin{aligned}\sin(65^{\circ} )& = \dfrac{x}{16}\\0.906307787 \cdot 16& = x\\x&=14.5\end{aligned}}

Thus, the length of the side BC is \boxed{14.5\:\text{cm}}.

Learn More:

1. Learn more about speed, distance and time brainly.com/question/2898741

2. Learn more about linear equation application brainly.com/question/2479097

3. Learn more about percentages brainly.com/question/8577699

Answer Details:

Grade: Middle School

Subject: Mathematics

Chapter: Trigonometry

Keywords: trigonometry, right angle, base, height, hypotenuse, sine, triangle, \theta, length, side, angles.

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