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Inessa [10]
3 years ago
10

Find the missing value and round to the nearest hundredth.

Mathematics
1 answer:
yarga [219]3 years ago
8 0
You have to use Trigonometric ratios here. I'll help you with a question, and you try to do the other two.

a. You are given the hypotenuse, and told to figure out the opposite. The trigonometric function that deals with that is sin(x), which is opposite over hypotenuse. So:
sin(51)= \frac{y}{12}

Solve for y:
y = 12sin(51)

Simplify:
y = 8.043

For these problems, you have to remember the ratios Sine, Cosine, and Tangent. An easy way is to make a mnemonic device. A good one that a lot of people use is SohCahToa. Which is Sine (Opposite, Hypotenuse), Cosine (Adjacent, Hypotenuse) and Tangent (Opposite, Adjacent). Remember trigonometry is just a glorified field of ratios of sides to angles. There are many more trigonometric ratios including inverse trigonometric ratios, reciprocal trigonometric ratios, and hyperbolic trigonometric ratios (which show up during differential calculus). But for now, focus on this. Haha.


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Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric recei
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Answer:

Abel receives $60, and Cedric receives $120

Step-by-step explanation:

Let Abel's share = A

Let Cedric's share = C

we are given the following

A + C = 180  - - - - - (1)   (Abel and Cedric will share a total of $180)

A = \frac{C}{2}\ - - - - - - - (2) (Abel will receive half as much as Cedric. )

from equation 2:

A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)

putting this value of C in eqn (3) into eqn (1)

A + (2A) = 180

3A = 180

∴ A = 180 ÷ 3 = 60

to find C, let us replace the value of A in eqn (3) with 60

C = 2A - - - - (3)

C = 2 × 60

C = 120

Therefore, Abel receives $60, and Cedric receives $120

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The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:

6= πd and then divide both sides of the equation by π you get that d = 1.90

To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:

1 = 0.9549θ.  

If you divide both sides of the equation by 0.9549 you get θ = 1.047197 radians.  

The question asked for the angle measure in degrees so you would need to convert the angle measure to degrees by multiplying the degree measurement by 180/π

1.047197 x 180/π =  60°

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3 years ago
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