Question
Given: \( A B C \) is a right triangle with right angle \( C . A C=15 \) centimeters and \( m \angle A=40^{\circ} \) What is \( B C \) ? Enter your answer, rounded to the nearest tenth, in the box. cm
Ask by Wyatt Bradley. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( BC \approx 12.6 \) cm
Solution
To find \( BC \) in the right triangle \( ABC \) with right angle at \( C \), you can use the tangent function, which relates the opposite side to the adjacent side relative to angle \( A \).
Given:
- \( \angle A = 40^\circ \)
- \( AC = 15 \) cm (adjacent to angle \( A \))
Using the tangent function:
\[
\tan(40^\circ) = \frac{BC}{AC}
\]
\[
BC = AC \times \tan(40^\circ)
\]
\[
BC = 15 \times \tan(40^\circ) \approx 15 \times 0.8391 \approx 12.5865 \text{ cm}
\]
Rounded to the nearest tenth:
\[
BC \approx 12.6 \text{ cm}
\]
**Answer:**
12.6 cm
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the length \( BC \) in triangle \( ABC \), we can use the sine function because we know the length of side \( AC \) and the angle \( A \). Using the sine definition: \[ \sin(A) = \frac{opposite}{hypotenuse} \] In this case, \( \sin(40^\circ) = \frac{BC}{AC} \), where \( AC = 15 \) cm. Rearranging gives us: \[ BC = AC \cdot \sin(A) = 15 \cdot \sin(40^\circ) \] Now we can calculate \( \sin(40^\circ) \) which is approximately 0.6428, so: \[ BC \approx 15 \cdot 0.6428 \approx 9.642 \, \text{cm} \] Rounded to the nearest tenth, \( BC \approx 9.6 \) cm.
