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2 years ago

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Trigonometry

1 answer:

Mazyrski [523]2 years ago

3 0

Answer:

0.3491rad

Step-by-step explanation:

We are asked to convert 20° to radians.

#We know that 1° is equal to π/180 or 0.01745rad.

To convert any angle degrees to radians, we multiply it by π/180:

$=20\times\pi/180\\\\=0.3491 \ or \ \frac{\pi}{9}rad$

Hence, 20° converted to radians is 0.3491rad

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Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

8 0

2 years ago

Please help me with number 12!

Olegator [25]

The answer is 10 quarters because 10 quarters would be $2.50. You would need 3 more nickles to get $2.65. 10 would be 7 more than 3.

4 0

3 years ago

Nichol walks at a constant pace of 1.2 m/s and takes 15 minutes to get to school.

liraira [26]

Answer:

The difference between the distances they walked is 600 meters.

Step-by-step explanation:

Let's calculate the distance traveled by Nichol and Sakura with the following equation:

$d = v*t$

Where:

v: is the speed

t: is the time

The distance traveled by Nichol is:

$d_{n} = 1.2 m/s*15min*\frac{60 s}{1 min} = 1080 m$

And the distance traveled by Sakura is:

$d_{s} = 1.4 m/s*20 min*\frac{60 s}{1 min} = 1680 m$

Hence, the difference between the distances they walked is:

$d_{t} = d_{s} - d_{n} = 1680 m - 1080 m = 600 m$

Sakura traveled 600 meters more than Nichol.

Therefore, the difference between the distances they walked is 600 meters.

I hope it helps you!

4 0

2 years ago

What is the solution ? Please help with this !!

FromTheMoon [43]

Answer:

the answer is c

Step-by-step explanation:

see picture

7 0

2 years ago

If f(x)f(x) is an exponential function where f(-0.5)=27f(−0.5)=27 and f(1.5)=21f(1.5)=21, then find the value of f(0.5)f(0.5), t

vovikov84 [41]

Given:

f(x) is an exponential function.

$f(-0.5)=27$

$f(1.5)=21$

To find:

The value of f(0.5), to the nearest hundredth.

Solution:

The general exponential function is

$f(x)=ab^x$

For, x=-0.5,

$f(-0.5)=ab^{-0.5}$

$27=ab^{-0.5}$ ...(i)

For, x=1.5,

$f(1.5)=ab^{1.5}$

$21=ab^{1.5}$ ...(ii)

Divide (ii) by (i).

$\dfrac{21}{27}=\dfrac{ab^{1.5}}{ab^{-0.5}}$

$\dfrac{7}{9}=b^2$

Taking square root on both sides, we get

$\dfrac{\sqrt{7}}{3}=b$

$b\approx 0.882$

Putting b=0.882 in (i), we get

$27=a(0.882)^{-0.5}$

$27=a(1.0648)$

$\dfrac{27}{1.0648}=a$

$a\approx 25.357$

Now, the required function is

$f(x)=25.357(0.882)^x$

Putting x=0.5, we get

$f(0.5)=25.357(0.882)^{0.5}$

$f(0.5)=23.81399$

$f(0.5)\approx 23.81$

Therefore, the value of f(0.5) is 23.81.

6 0

2 years ago