Question

QUESTION 1 Find the remaining sides of a 30° -60°-90° triangle if the shortest side is 3.

Answer 1

Answer:

the other sides are 6 and 3√3

Step-by-step explanation:

Answer 2

Answer:

x = 6

Step-by-step explanation:

Right Triangle

We are given a right triangle whose shortest side has a length of 3 units. This side must be opposite to the smallest acute angle of 30°.

The triangle is shown in the figure attached.

The tangent ratio relates the opposite side with the adjacent side. The formula can be applied to the angle of 30° as follows:

$\displaystyle \tan 30^\circ=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 30^\circ=\frac{3}{y}$

Solving for y:

$\displaystyle y=\frac{3}{\tan 30^\circ}$

Since:

$\tan 30^\circ=\frac{1}{\sqrt{3}}$

$\displaystyle y=3\sqrt{3}$

Now applying the sine to find the hypotenuse x:

$\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 30^\circ=\frac{3}{x}$

Solving for x:

$\displaystyle x=\frac{3}{\sin 30^\circ}$

Since:

$\sin 30^\circ=\frac{1}{2}$

$\displaystyle x=\frac{3}{\frac{1}{2}}$

x = 6