A partir de lo anterior, ¿cuál es la altura h del triángulo?
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Understand the Problem
La pregunta nos pide calcular la altura 'h' de un triángulo rectángulo dado su base (4 cm) y uno de sus ángulos agudos (38 grados). Para resolverlo, aplicaremos la función trigonométrica tangente.
Answer
c) 3.1 cm
Answer for screen readers
c) 3.1 cm
Steps to Solve
- Identify the trigonometric relationship
We know the angle ($38^\circ$) and the adjacent side (4 cm), and we want to find the opposite side (h). Therefore, we use the tangent function:
$tan(\theta) = \frac{opposite}{adjacent}$
- Set up the equation
$tan(38^\circ) = \frac{h}{4}$
- Solve for $h$
Multiply both sides by 4:
$h = 4 \cdot tan(38^\circ)$
- Calculate the value of $h$
Using a calculator, $tan(38^\circ) \approx 0.7813$
$h \approx 4 \cdot 0.7813$ $h \approx 3.125$
- Choose the closest answer
The closest answer from the available options is 3.1 cm.
c) 3.1 cm
More Information
The height $h$ of the triangle is approximately 3.1 cm.
Tips
A common mistake is using the wrong trigonometric function (sine or cosine instead of tangent) or incorrectly setting up the ratio of sides.
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