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3 years ago

Use triangleABC to find the value of sin B

Mathematics

2 answers:

klasskru [66]3 years ago

7 0

The given triangle is a right triangle right angled at angle C. For angle B the adjacent side is BC ,the side opposite to angle B is AC while AB is hypotenuse. Sin of any angle is ratio of opposite and hypotenuse.

Sin $\frac{opposite}{hypotenuse}$

The opposite in the figure is 24 and hypotenuse is 25

Substituting the values of opposite and hypotenuse from figure we have:

Sin B= $\frac{24}{25}$

Delicious77 [7]3 years ago

4 0

As we are given

Opposite side of the angle B=24

Hypotenuse =25

$\\ \ sin \theta=\frac{Opposite}{Hypotenuse}\\ \\ \ SinB=\frac{24}{25}\\$

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A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

Marat540 [252]

Answer-

After 76 swings the angle through which it swings less than 1°

Solution-

From the question,

Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.

So the angle of the second swing = $(30\times \frac{95}{100})^{\circ}$

Then the angle of third swing = $(30\times (\frac{95}{100})^2)^{\circ}$

So, this follows a Geometric Progression.

$(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)$

a = The initial term = 30

r = Common ratio = $\frac{95}{100}$

As we have to find the number swings when the angle swept by the pendulum is less than 1°.

So we have the nth number is the series as 1, applying the formula

$T_n=ar^{n-1}$

Putting the values,

$\Rightarrow 1=30(\frac{95}{100})^{n-1}$

$\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}$

Taking logarithm of both sides,

$\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}$

$\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})$

$\Rightarrow -1.5=(n-1)(-0.02)$

$\Rightarrow 1.5=(n-1)(0.02)$

$\Rightarrow n-1=\dfrac{1.5}{0.02}$

$\Rightarrow n-1=75$

$\Rightarrow n=76$

Therefore, after 76 swings the angle through which it swings less than 1°

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Pani-rosa [81]

Answer:

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