Question

If the triangle shown, The angle CAB = 30° and AC =50m. What is the length of BC is?

Answer 1

GIVEN:

We are given a right angle as shown in the attached image. For triangle ABC, we have;

$\angle A=30\degree,\text{ }AC=50m$

Required;

To find the length of side AC.

Step-by-step solution;

For a right angled triangle with respect to the reference angle, the sides are labeled as follows;

$\begin{gathered} Reference\text{ }angle=30\degree \\ \\ Opposite=BC \\ \\ Adjacent=AB \\ \\ Hypotenuse=AC \end{gathered}$

To find the length of BC (opposite), given the length of AC (hypotenuse), we shall use the ratio;

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

We now use the values provided and we have;

$sin30\degree=\frac{BC}{50}$

Now we cross multiply;

$\begin{gathered} 50\times sin30=BC \\ \\ 50\times0.5=BC \\ 25=BC \\ \end{gathered}$

ANSWER:

$BC=25$