Question

Use the correct trigonometric function to solve for both x and y .

Answer 1

As per given by the question.

There are given that a triangle.

Now,

Suppose given triangle is ABC.

Then, redraw the given triangle.

Now,

For finding the value of x, and y;

First find the value of x with the help of sine trigonometric function.

So,

$\sin 35^{\circ}=\frac{AB}{AC}$

Then,

Substitute the value x for AB and 22 for AC.

SO,

$\begin{gathered} \sin 35^{\circ}=\frac{AB}{AC} \\ \sin 35^{\circ}=\frac{x}{22} \\ 0.57=\frac{x}{22} \\ x=0.57\times22 \\ x=12.54 \end{gathered}$

Now,

For finding the value of y,

Here, use pythagoras theorem in triangle ABC.

So, from the pythagoras theorem;

$AB^2+BC^2=AC^2$

Then,

Substitute the value in above formula;

So,

$\begin{gathered} AB^2+BC^2=AC^2 \\ x^2+y^2=(22)^2 \end{gathered}$

Now, put the value 12.54 for x,

So,

$\begin{gathered} x^2+y^2=(22)^2 \\ (12.54)^2+y^2=(22)^2 \\ 157.25+y^2=484 \\ y^2=484-157.25 \\ y^2=326.75 \end{gathered}$

Then,

$\begin{gathered} y^2=326.75 \\ y=\sqrt[]{326.75} \\ y=18.076 \end{gathered}$

Hence, the value of x is 12.54 and the value of y is 18.076.