To find the length of side \( b \) in triangle \( ABC \), we can use the formula for the area of a triangle given two sides and the included angle:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
Where:
- Area is given as \( 528.3 , \text{mm}^2 \)
- \( a = 21 , \text{mm} \)
- \( \angle C = 57^\circ \)
We can rearrange the formula to solve for \( b \):
\[ b = \frac{2 \times \text{Area}}{a \times \sin(C)} \]
- Substitute the known values into the formula:
\[ b = \frac{2 \times 528.3}{21 \times \sin(57^\circ)} \]
- Calculate \( \sin(57^\circ) \):
Using a calculator, we find:
\[ \sin(57^\circ) \approx 0.8387 \]
- Now, plug in all the numbers:
\[ b = \frac{2 \times 528.3}{21 \times 0.8387} \] \[ b = \frac{1056.6}{17.6327} \] \[ b \approx 59.9 , \text{mm} \]
Rounding to the nearest tenth, we get:
\[ \boxed{59.9} , \text{mm} \]
1 answer