In ΔEFG, the measure of ∠G=90°, the measure of ∠E=59°, and FG = 8.1 feet. Find the length of GE to the nearest tenth of a foot.

The length of GE is 4.9ft

Step-by-step explanation:

In this question, we are asked to calculate the length of GE

Kindly note that since one of the angles in the triangle is equal to 90°, this means that we are dealing with a right angled triangle.

Please, kindly check the attachment for the diagram.

Firstly, since it is a right-angled triangle, we identify the following.

The hypotenuse is the length EF, the opposite is the length FG while the adjacent is the length GE

To calculate the GE which is the adjacent, we employ the use of trigonometric identities.

Since we are dealing with the adjacent and the opposite, the correct trigonometric identity to use is the tangent

Mathematically, by definition, the tangent of an angle = length of the opposite/length of the adjacent

With specific reference to the question at hand;

⇒ Tan 59° = 8.1/GE

GE = 8.1/Tan 59° = 4.9ft (to the nearest tenth of a foot

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