Question

note: images are not drawn to scale.
△abc ~ △def ~ △ghi
what is tan h?
tan h = □

Explanation:

Step1: Recall the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\sim\triangle GHI\), their corresponding angles are equal. So, \(\angle H=\angle B=\angle E\).

Step2: Recall the definition of tangent

For a right - angled triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). In \(\triangle ABC\), \(\tan B = \frac{AC}{AB}\). Given \(AC = 120\) and \(AB=90\).

Step3: Calculate \(\tan B\)

\(\tan B=\frac{120}{90}=\frac{4}{3}\). Since \(\angle H=\angle B\), \(\tan H=\tan B\).

Answer:

\(\frac{4}{3}\)