Construct a right-angled triangle containing an angle A such that sin A = 0.4 - Junior Cycle Mathematics - Question a - 2012

To construct a right-angled triangle with angle A satisfying sin A = 0.4, we recall that:

$ext{sin A} = \frac{\text{opposite}}{\text{hypotenuse}}$

Let the length of the opposite side be 4 units. Then, the hypotenuse (h) can be found as follows:

$h = \frac{4}{0.4} = 10$

Now, to find the adjacent side (b), we can use the Pythagorean theorem:

$a^2 + b^2 = h^2$

Substituting for a (opposite side) and h:

$4^2 + b^2 = 10^2$

$16 + b^2 = 100$

$b^2 = 100 - 16 = 84$

Hence, the length of the adjacent side is:

$b = \sqrt{84} = 2\sqrt{21}$

The triangle is now constructed with sides of 4, 10, and $2\sqrt{21}$.