Question

Solve for the missing sides 30-60-90 triangle show work please and thank you

Answer 1

Answer:

4.

$x=8\sqrt{3}$

$y=16$

5.

$x=3$

$y=3\sqrt{3}$

Step-by-step explanation:

The sides of a (30 - 60 - 90) triangle follow the following proportion,

$a-a\sqrt{3}-2a$

Where (a) is the side opposite the (30) degree angle, ($a\sqrt{3}$) is the side opposite the (60) degree angle, and (2a) is the side opposite the (90) degree angle. Apply this property for the sides to solve the two given problems,

4.

It is given that the side opposite the (30) degree angle has a measure of (8) units. One is asked to find the measure of the other two sides.

The measure of the side opposite the (60) degree side is equal to the measure of the side opposite the (30) degree angle times ($\sqrt{3}$). Thus the following statement can be made,

$x=8\sqrt{3}$

The measure of the side opposite the (90) degree angle is equal to twice the measure of the side opposite the (30) degree angle. Therefore, one can say the following,

$y=16$

5.

In this situation, the side opposite the (90) degree angle has a measure of (6) units. The problem asks one to find the measure of the other two sides,

The measure of the side opposite the (60) degree angle in a (30-60-90) triangle is half the hypotenuse times the square root of (3). Therefore one can state the following,

$y=3\sqrt{3}$

The measure of the side opposite the (30) degree angle is half the hypotenuse (the side opposite the (90) degree angle). Hence, the following conclusion can be made,

$x=3$