Question

the measure of an inclined angle between two sides is 45° and the measure of the sides are 5m and 8m. find the measure of the third side.

Answer 1

EXPLANATION

We can represent the states in the following picture:

We can apply a Trigonometric ratio in order to get the value of the third side, assuming that it is called x:

$\sin45=\frac{Opposite\text{ cathetus}}{Hypotenuse}=\frac{x}{8}$

Multiplying both sides by 8:

$8*\sin45=x$

Switching sides:

$x=8*\sin45$

Multiplying terms:

$x=4\sqrt{2}$

In conclusion, the measure of the third side is approximately equivalent to 4√2 or 5.65