Question

Please answer quick!

Answer 1

9.95

Side x is opposite angle 56 degrees

12 in is the hypotenuse. We will use

Sine = opposite/hypotenuse to find x.

Sine(56) = x/12. (Make sure calculator is in degree mode)

0.829038 = x/12. Then multiply each side by 12.

12(0.829038) = (×/12)(12)

x=9.95 in

Answer 2

D. 9.95 in

Explanation:

Pre-Solving

We are given the right triangle ABC. We know that m∠B is 56°, the length of AB is 12 in, and the length of AC is x.

We want to find the value of x.

We can use trigonometry to find it.

Recall the three trigonometric functions:

• sine (sin), which is
  `(opposite)/(hypotenuse)`.
• cosine (cos), which is
  `(adjacent)/(hypotenuse)`.
• tangent (tan), which is
  `(opposite)/(adjacent)`.

Also recall that when labeling which side is which, we need to have them in reference to a certain angle - it makes sense to make that reference angle ∠B.

So, in reference to ∠B, the opposite side is AC, the adjacent side is CB, and the hypotenuse is AB.

Because we need the value of AC and AB (the opposite and hypotenuse), we will use sine.

Solving

The sine of 56° is equal to
`(AC)/(AB)`.

This can be rewritten as:

`sin(56)=(AC)/(AB)`

Substitute the values we know into the equation.

`sin(56)=(x)/(12)`

Now, multiply both sides by 12.

12 × sin(56) = x

12sin(56)=x

Now, plug 12sin(56) into your calculator. Make sure that your calculator is in degree mode.

9.95 in ≈ x (rounded to the nearest hundredth).

So, the answer is D.