Question

Can someone help me Using the trigonometric ratios, solve for the missing sides x and y of each right triangle. Round your answers to the nearest tenth.

Answer 1

Given,

The measue of one side is 19.

The measure of one angle is 80 degree.

Required

The value of x and y.

a)By trigonometric ratio,

`\begin{gathered} sin80^(\circ)=(19)/(x) \\ x=(19)/(sin80^(\circ)) \\ x=19.3 \end{gathered}`

The value of y is calculatedby using cosine,

`\begin{gathered} cos80^(\circ)=(y)/(19.29) \\ y=cos80^(\circ)*19.29 \\ y=3.4 \end{gathered}`

Hence, the value of x is 19.3 and y is 3.4.

b)By trigonometric ratio,

`\begin{gathered} sin45^(\circ)=(y)/(27) \\ y=sin45^(\circ)*27 \\ y=19.1 \end{gathered}`

The value of x is calculatedby using cosine,

`\begin{gathered} cos45^(\circ)=(x)/(27) \\ x=cos45^(\circ)*27 \\ x=19.1 \end{gathered}`

Hence, the value of x is 19.1 and y is 19.1.