Question

HELP!!! What are the exact measures of the other two sides of the triangles

? Use special right triangle ratio and show your work.

Answer 1

In the given triangle with AC=20 and C=30, the measures of the other two sides are:

AB=10

BC=10 √3

In a right triangle with a 30-degree angle, we can use the special right triangle ratios to find the lengths of the sides. In this case, we're dealing with a 30-60-90 triangle. The ratio of the sides in a 30-60-90 triangle is

1: √3 :2.

Let's label the sides of the triangle as follows:

The side opposite the 30-degree angle is the shorter leg (let's call it a).

The side opposite the 60-degree angle is the longer leg (let's call it b).

The hypotenuse is opposite the 90-degree angle (let's call it c).

For a 30-60-90 triangle:

a:b:c=1: √3 :2

Given that c=20, we can find a and b using the ratios. Let's set up the proportions:

1: √3 :2=a:b:20

To find a, multiply both sides of the proportion by 1:

a=1×
`(20)/(2)`​ =10

To find b, multiply both sides of the proportion by √3 :

b= √3 ×
`(20)/(2)` =10 √3

​So, in the given triangle with AC=20 and C=30, the measures of the other two sides are:

AB=10

BC=10 √3