Question

Find the length of AC Use that length to find the length of

Answer 1

Answer:

1. AC = 5 cm

2. CD = 10.7 cm

Step-by-step explanation:

Looking at the left triangle, we see that AC is the side "opposite" of the angle given and AB is the "hypotenuse".

Which trigonometric ratio relates "opposite" to "hypotenuse"?

Yes, that's SINE.

So we can write:

$Sin(30)=\frac{AC}{10}\\AC=10*Sin(30)$

We know from 30-60-90 triangle, Sin(30) = 0.5, so we have:

$AC=10*Sin(30)\\AC=10*0.5\\AC=5$

Thus,

AC = 5 cm

Now, looking at right side triangle, we know AC, side "opposite" and we want to find CD, side "adjacent". Which trig ratio relates these 2 sides?

Yes, that's tan!

Thus we can write:

$Tan(25)=\frac{5}{CD}\\CD=\frac{5}{Tan(25)}$

Now using calculator, we get our answer to be:

CD = $\frac{5}{Tan(25)}=10.7$

So

CD = 10.7 cm