+308 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.
+2666 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?
+2666 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?
