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

What is the length of co? Round to the nearest tenth!
CO.
23 cm
40 cm
10.7 cm
18.6 cm
10 cm
30°

Find the length of AC Use that length to find the length of What is the length of-example-1
User Herolover
by
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1 Answer

4 votes

Answer:

1. AC = 5 cm

2. CD = 10.7 cm

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)=(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)=(5)/(CD)\\CD=(5)/(Tan(25))

Now using calculator, we get our answer to be:

CD =
(5)/(Tan(25))=10.7

So

CD = 10.7 cm

User Anamari
by
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