Question

What is the value of each variable?Xy60°16X =y0084:: 8√2:: 8√3:: 4√2:: 4√3

Answer 1

GIVEN:

We are given a right angled triangle with sides and angles as indicated.

Required;

We are required to use the information given to calculate the missing sides, x and y.

Step-by-step solution:

We have a right angled triangle with the reference angle given as 60 degrees. Therefore, the sides will be labelled as follows;

$\begin{gathered} x=opposite \\ y=adjacent \\ 16=hypotenuse \end{gathered}$

To calculate the side labeled x, we would use the trig ratio which is,

$sin\theta=\frac{opposite}{hypotenuse}$

Therefore;

$sin60\degree=\frac{x}{16}$

We shall apply the values of special angles. For a trigonometric calculation with right angled triangles,

$sin60\degree=\frac{\sqrt{3}}{2}$

The equation can now be refined and written as follows;

$\frac{\sqrt{3}}{2}=\frac{x}{16}$

Now we cross multiply;

$\begin{gathered} \frac{16\sqrt{3}}{2}=x \\ \\ 8\sqrt{3}=x \end{gathered}$

Next we calculate the value of y. We shall use the ratio;

$cos\theta=\frac{adjacent}{hypotenuse}$

Hence;

$cos60\degree=\frac{y}{16}$

The cosine of 60 degrees is,

$cos60\degree=\frac{1}{2}$

We substitute this into the equation above;

$\begin{gathered} \frac{1}{2}=\frac{y}{16} \\ \\ Cross\text{ }multiply; \\ \\ \frac{16\times1}{2}=y \\ \\ 8=y \end{gathered}$

Therefore the missing sides are;

ANSWER:

$\begin{gathered} x=8\sqrt{3} \\ \\ y=8 \end{gathered}$

x = 8√3

y = 8