Question

I just need the answer you dont have to explain deeply

Answer 1

Given the right triangle ABC, you know the measure of ∠B and the length of the side across it (AC), to determine the length of the hypothenuse (AB) you have to use trigonometric ratios, in this case, the sine, which is defined as follows:

`\sin \theta=(opposite)/(hypothenuse)`

Where

θ is the angle, in this case, ∠B

"opposite" refers to the side across the angle, in this case, side AC

"hypothenuse" is the longest side of the triangle, in this case, side AB

Given:

∠B=57º

AC=10.8

AB= x

`\begin{gathered} \sin B=(AC)/(AB) \\ \sin 57=(10.8)/(x) \end{gathered}`

From this expression, you can determine the value of x.

- Multiply both sides by x

`\begin{gathered} x\cdot\sin 57=x\cdot(10.8)/(x) \\ x\cdot\sin 57=10.8 \end{gathered}`

-Divide both sides by the sine of 57º

`\begin{gathered} (x\cdot\sin57)/(\sin57)=(10.8)/(\sin57) \\ x=12.877\cong12.9 \end{gathered}`

The length of AB is 12.9 units