Mathematics, 29.06.2019 13:30 georgehall9795

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Answer from: firenation18

By the law of sines,

$\dfrac{\sin m\angle A}a=\dfrac{\sin m\angle B}b\implies\sin m\angle B=\dfrac{33.7\sin75^\circ}{51.2}$

We get one solution by taking the inverse sine:

$m\angle B=\sin^{-1}\dfrac{33.7\sin75^\circ}{51.2}\approx39^\circ$

In this case there is no other solution!

To check: suppose there was. The other solution is obtained by recalling that $\sin(180-x)^\circ=\sin x^\circ$ for all , so that

$180^\circ-m\angle B=\sin^{-1}\dfrac{33.7\sin75^\circ}{51.2}\implies m\angle B\approx141^\circ$

But remember that the angles in any triangle must sum to 180 degrees in measure. This second "solution" violates this rule, since two of the known angles exceed 180: 75 + 141 = 216 > 180. So you're done.

Answer from: hjgdk2167

This triangle is not a right triangle. How do we solve this then? You will use the law of sine with is shown below:

$\frac{sin A}{a} =\frac{sin B}{b} = \frac{sinC}{c}$

What we know is shown in the image attached below:

Plug what you know into the law of sine

$\frac{sin75}{51.2} =\frac{sinB}{33.7}$

To solve for sinB cross multiply

sin75*33.7 = sinB * 51.2

32.55 = sinB*51.2

Divide 51.2 to both sides to isolate sinB

32.55 / 51.2 = sinB / 51.2

0.63577 = sinB

To find B you must use arcsin:

$sin^{-1} 0.63577$

39.477

^^^This is your rough estimate but you can simply keep it to 39 degrees

This means that your answer is correct!

Hope this helped!

I've posted this already but no one is answering so i'm posting for more points.

Answer from: Quest

Polar coordinates is 8,9

Answer from: Quest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

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