Pregunta
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
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( BC \approx 12.6 \) cm
Solución
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
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución 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.
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