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

  1. 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:

$tan(\theta) = \frac{opposite}{adjacent}$

  1. Set up the equation

$tan(38^\circ) = \frac{h}{4}$

  1. Solve for $h$

Multiply both sides by 4:

$h = 4 \cdot tan(38^\circ)$

  1. Calculate the value of $h$

Using a calculator, $tan(38^\circ) \approx 0.7813$

$h \approx 4 \cdot 0.7813$ $h \approx 3.125$

  1. 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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