The length of the side opposite the 90 degree angle of a 30-60-90 is 18 ft. Determine the lengths of the other two sides. Round your answer to the nearest hundredth when necessary.
- The side opposite the 30 degree angle is ___ ft.
- The side opposite the 60 degree angle is ___ ft.

The side opposite 30 is 9 ft.

The side opposite 60 is 15.59 ft.

Step-by-step explanation:

Below are pictures of how I got the answer.

I will provide steps to accompany each corresponding picture to further explain what I am doing.

1. This picture simply illustrates what the triangle looks like. The Hypotenuse is 18, as described in the problem.

2. I am showing how the sin will work. What is the opposite side and what is the hypotenuse. I picked this particular angle because it allow me to divide it by a number I already have, 18. I show that sin of 30 is 0.5

3. Now, we know what the side value is, 9. We can easily find the remaining side using Pythagorean theorem.

9^2 + y^2 =18^2

81 + y^2 = 324

y^2 = 243

y = 15.59

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

yes

step-by-step explanation: