Question

Find the measurement of each side indicated and round to the nearest tenth for both triangles

Answer 1

a) We have a right triangle.

We have to find the value of x, which is the hypotenuse.

We can relate the angle B, the side AC and x with a trigonometric ratio as:

`\begin{gathered} \sin (B)=\frac{\text{Opposite}}{\text{Hypotenuse}}=(AC)/(AB) \\ \sin (57\degree)=(10.8)/(x) \\ x=(10.8)/(\sin (57\degree)) \\ x\approx(10.8)/(0.83867) \\ x\approx12.9 \end{gathered}`

b) In this case, x is the adyacent side to angle A.

We can relate the sides and the angle as:

`\begin{gathered} \cos (A)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=(AC)/(AB) \\ \cos (47\degree)=(x)/(3) \\ x=3\cdot\cos (47\degree) \\ x\approx3\cdot0.682 \\ x\approx2.0 \end{gathered}`

Answer:

a) x = 12.9

b) x = 2.0