I can help you with the math worksheet. For question 2, you need to use the sine and cosine functions to find the lengths of the sides a and b. Here are the steps:
- Label all angles and sides. The angle opposite to the side c is 90 degrees, so it is a right angle. The angle opposite to the side a is 30 degrees, so it is given in the question. The angle opposite to the side b is the remaining angle of the triangle, so it is 180 - 90 - 30 = 60 degrees.
- Use the sine function to find the length of the side a. The sine function relates an angle of a right triangle to the ratio of the opposite side and the hypotenuse. So, we have sin(30) = a/c. We know that c is 10, so we can solve for a by multiplying both sides by 10. We get a = 10 * sin(30). Using a calculator, we can find that sin(30) is 0.5, so a = 10 * 0.5 = 5. The length of the side a is **5 units**.
- Use the cosine function to find the length of the side b. The cosine function relates an angle of a right triangle to the ratio of the adjacent side and the hypotenuse. So, we have cos(30) = b/c. We know that c is 10, so we can solve for b by multiplying both sides by 10. We get b = 10 * cos(30). Using a calculator, we can find that cos(30) is about 0.866, so b = 10 * 0.866 = 8.66. The length of the side b is **8.66 units**.
For question 3, you need to use the tangent function to find the height of the tree. The tangent function relates an angle of a right triangle to the ratio of the opposite side and the adjacent side. So, we have tan(35) = h/20, where h is the height of the tree and 20 is the distance from the tree to where you are standing. We can solve for h by multiplying both sides by 20. We get h = 20 * tan(35). Using a calculator, we can find that tan(35) is about 0.7, so h = 20 * 0.7 = 14. The height of the tree is **14 meters**.
I hope this helps you with your math homework. If you have any other questions, please feel free to ask me