Trigonometry, Law of Sines and Cosines

Question

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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.

notsmart2.0 May 14, 2022

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

BuilderBoi · Answer 1 · 2022-05-14T11:15:00

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?

BuilderBoi · Answer 2 · 2022-05-14T11:18:02

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?