Question

In ΔFGH, the measure of ∠H=90°, HG = 48, FH = 55, and GF = 73. What ratio represents the tangent of ∠G?

Answer 1

55:48

Explanation:

Given a right angles triangle ∆FGH

where ∠H=90°, HG = 48, FH = 55, and GF = 73,

Based on the diagram attached

To find the tangent of angle G, we will use the concept of SOH CAH TOA in trigonometry identity.

According to TOA:

Tan ∠G = Opposite/Adjacent

Note that the opposite side will be the side facing the angle we are considering i.e ∠G

Opposite = 55

Adjacent will be the base of the triangle = 48

Tan∠G = 55/48

The ratio that represents the tangent of ∠G is 55:48

Answer 2

55/48

Explanation:

We can find the tangent of ∠G using the trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Considering triangle ΔFGH, where ∠H=90°

The opposite side is FH, the hypotenuse side is GF and the adjacent side is HG hence,

Tan ∠G = FH/HG

= 55/48