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# Trigonometry, Law of Sines and Cosines

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1. Find BC.

2. Find AC.

3. In triangle ABC, CA=4sqrt(2), CB=4 sqrt(3), and A=60 degrees. What is B in degrees?

4. Find AC.

5. Find sin B.

6. Find cos A.

7. In triangle ABC, sin A = 4/5. Find cos B.

8. Find DB.

May 14, 2022
edited by notsmart2.0  May 14, 2022
edited by notsmart2.0  May 14, 2022

#1
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1) Using the law of cosines, we have: $$c^2 = 6^2 + {7\sqrt2}^2 -2\times 6 \times 7 \sqrt 2 \cos 45$$

Simplifying, we have $$c^2 = 36 + 98 - 84 \sqrt 2 \times { \sqrt 2 \over 2}$$, which simplifies to: $$c^2 = 50$$

Can you take it from here?

May 14, 2022
#2
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5) Using the Pythagorean Theorem on $$\triangle ADC$$, we find that $$\overline{AD} = 8$$

Now, applying the Pythagorean Theorem on $$\triangle ADB$$, we find that $$\overline{AB} = 17$$.

We also know that $$\sin = {\text{opposite} \over \text{hypotenuse}}$$, which in this case, is $${\overline{AD}} \over {\overline{AB}}$$.

Can you take it from here?

May 14, 2022