Question

Pls help ASAP! 20pts! What is the value of sin N? What is the value of x to the nearest tenth? What is the value of x to the nearest degree?

Answer 1

1.

`C.\\sin(N)=(√(3) )/(2)`

2.

`x=82.1`

3.

x = 18°

Explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle. When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

`sin(N)=(5√(3) )/(10) \\\\sin(N)=(√(3) )/(2)`

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent. If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side. Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

`tan(75)=(x)/(22)\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x`

3. Since we're now solving for an angle, we must using inverse trigonometry. We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ. We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side. Now we can do the inverse trig to find the measure of x:

`tan^-^1((11)/(33))=x\\ 18.43494882=x\\18=x`