Solve the triangle using the Law of Sines. (Assume c = 60, ∠A = 52°, and ∠B = 15°. Round lengths to two decimal places.)
a =	
b =	
∠C =	
 °


To solve this triangle using the Law of Sines, we will use the provided information:

- \( c = 60 \)
- \( \angle A = 52^\circ \)
- \( \angle B = 15^\circ \)

### Step 1: Find \( \angle C \)
Since the sum of all angles in a triangle is always \( 180^\circ \), we can calculate \( \angle C \) as:

\[
\angle C = 180^\circ - \angle A - \angle B
\]
\[
\angle C = 180^\circ - 52^\circ - 15^\circ = 113^\circ
\]

### Step 2: Apply the Law of Sines
The Law of Sines is:

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

We can now solve for \( a \) and \( b \).

#### Solve for \( a \):

\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
\[
a = \frac{c \cdot \sin A}{\sin C}
\]
\[
a = \frac{60 \cdot \sin 52^\circ}{\sin 113^\circ}
\]
\[
a \approx \frac{60 \cdot 0.78801}{0.92050} \approx 51.36
\]

#### Solve for \( b \):

\[
\frac{b}{\sin B} = \frac{c}{\sin C}
\]
\[
b = \frac{c \cdot \sin B}{\sin C}
\]
\[
b = \frac{60 \cdot \sin 15^\circ}{\sin 113^\circ}
\]
\[
b \approx \frac{60 \cdot 0.25882}{0.92050} \approx 16.87
\]

### Final Answer:
- \( a \approx 51.36 \)
- \( b \approx 16.87 \)
- \( \angle C = 113^\circ \)

Would you like any further details or explanations?

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**Related questions**:
1. How does the Law of Sines differ from the Law of Cosines in triangle problems?
2. What happens if two angles and a non-included side are given in a triangle?
3. Can the Law of Sines be used for all types of triangles?
4. What is the ambiguous case in the Law of Sines?
5. How can the Law of Cosines be used to solve a triangle?

**Tip**: Always check the sum of the angles when solving triangles, as this helps catch errors early.

Solve the triangle using the Law of Sines. (Assume c = 60, ∠A = 52°, and ∠B = 15°. Round lengths to two decimal places.) a = b = ∠C = °

Learn how to solve a triangle using the Law of Sines with given values c = 60, ∠A = 52°, and ∠B = 15°. This step-by-step guide includes finding unknown sides and angles and applying the Law of Sines formula. Suitable for high school trigonometry students.

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