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To find the missing sides \( x \) and \( y \) of the triangle, we can use the Law of Sines, which states:

\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]

### Given Information:
1. Angle A = 21°
2. Angle B = 37°
3. Side opposite to Angle B (side c) = 100
4. Angle C = 180° - 21° - 37° = 122°

Now, we will use the Law of Sines to find sides \( x \) and \( y \):

#### Step 1: Finding Side \( x \)

\[
\frac{x}{\sin 37°} = \frac{100}{\sin 122°}
\]

\[
x = \frac{100 \cdot \sin 37°}{\sin 122°}
\]

#### Step 2: Finding Side \( y \)

\[
\frac{y}{\sin 21°} = \frac{100}{\sin 122°}
\]

\[
y = \frac{100 \cdot \sin 21°}{\sin 122°}
\]

Now let's compute these values.The missing sides of the triangle, rounded to the nearest tenth, are:

- \( x \approx 71.0 \)
- \( y \approx 42.3 \)

Would you like more details on the solution or have any questions?

### Related Questions to Explore:
1. What is the Law of Cosines, and how does it differ from the Law of Sines?
2. How can you solve a triangle if all sides are known?
3. What are some practical applications of solving triangles in real life?
4. How do you determine if a triangle is right-angled using trigonometry?
5. How can trigonometry be applied to find the height of a building?

**Tip:** Always check if the angles add up to 180° in any triangle problem to avoid errors.

Find the missing sides x and y of the triangle using the Law of Sines. Given: Angle A = 21°, Angle B = 37°, and the side opposite to Angle B = 100.

Learn how to solve a triangle problem using the Law of Sines. Given angles of 21°, 37°, and a side length of 100, we compute the missing sides x and y. This problem covers key trigonometric concepts, suitable for students in Grades 10-12.

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