Question

find x in the following right - angled triangles.
ex.
sol x:4 = 2:1
x = 8
(1)
(2)
sol x:8=
2x=
x=
(3)

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 right - angled triangle, the ratio of the sides is $1:\sqrt{3}:2$, where the side opposite the 30° angle is the shortest, the side opposite the 60° angle is $\sqrt{3}$ times the shortest side, and the hypotenuse is 2 times the shortest side.

Step2: Solve for (1)

The side opposite the 30° angle is $2\sqrt{2}$, and $x$ is the hypotenuse. Since the hypotenuse is 2 times the side opposite the 30° angle in a 30 - 60 - 90 triangle, we have $x = 2\times2\sqrt{2}=4\sqrt{2}$.

Step3: Solve for (2)

In a 30 - 60 - 90 triangle, if the hypotenuse is 8 and $x$ is the side opposite the 30° angle, the ratio of the side opposite the 30° angle to the hypotenuse is $1:2$. So $x:8 = 1:2$, which gives $2x=8$, and $x = 4$.

Step4: Solve for (3)

The hypotenuse is 5 and $x$ is the side opposite the 30° angle. Using the ratio of the side opposite the 30° angle to the hypotenuse ($1:2$) in a 30 - 60 - 90 triangle, we have $x=\frac{5}{2}$.

Answer:

(1) $x = 4\sqrt{2}$
(2) $x = 4$
(3) $x=\frac{5}{2}$