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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
10. Roots and Zeros
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Exercise 63 Page 79

Use the trigonometric ratios to find AB.

AB=8sqrt(3)

Practice makes perfect

Let's identify the angles of â–³ ADC by the Interior Angles Theorem.

Here, we have a special triangle that is 30^(∘) - 60^(∘) - 90^(∘). To find AB which is equal to DC, we can use the trigonometric ratio tan30^(∘). tan 30^(∘)= AD/DC ⇔ tan 30^(∘)=1/sqrt(3) ⇓ AD/DC=1/sqrt(3) Let's substitute AD=8 in the identity and use cross multiplication to find DC.

AD/DC=1/sqrt(3)
Substitute

AD= 8

8/DC=1/sqrt(3)
CrossMult

Cross multiply

8sqrt(3)=DC
RearrangeEqn

Rearrange equation

DC=8sqrt(3)

Therefore, AB is also 8sqrt(3).

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