The diagram of the triangle is shown below
We would calculate EF by applying the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the triangle,
hypotenuse = EG = 10
one leg = FG = 4
other leg = EF
By applying the pythagorean theorem, we have
10^2 = 4^2 + EF^2
100 = 16 + EF^2
EF^2 = 100 - 16 = 84
Taking the square root of both sides of the equation,
[tex]EF\text{ = }\sqrt[]{84}\text{ = }\sqrt[]{4\times21}\text{ = }\sqrt[]{4}\times\sqrt[]{21}\text{ = 2}\sqrt[]{21}[/tex]
We would find CosE by applying the Cosine trigonometric ratio which is expressed as
Cos θ = adjacent side/hypotenuse
adjacent side = EF
[tex]\begin{gathered} \text{CosE = }\frac{2\sqrt[]{21}}{10} \\ \text{CosE = }\frac{\sqrt[]{21}}{5} \end{gathered}[/tex]
Sec G = 1/CosG
[tex]\begin{gathered} \text{Taking G as the reference angle, } \\ \text{adjacent side = GF = 4} \\ \text{CosG = }\frac{4}{10} \\ \text{CosG = }\frac{2}{5} \end{gathered}[/tex]
[tex]\text{ Sec G = }\frac{5}{2}[/tex]
We would find TanG by applying the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/hypotenuse
Taking angle G as the reference angle, opposite side = EF
[tex]\begin{gathered} \text{TanG = }\frac{2\sqrt[]{21}}{4} \\ Tan\text{ G = }\frac{\sqrt[]{21}}{2} \end{gathered}[/tex]
