For the given triangle, m∠G° = 51°, HI = 23.3 units, and GH = 18.9 units.
Step-by-step explanation:
Step 1:
In the triangle, the given angle is 39°, the hypotenuse side's length is 30 units. Assume the opposite side's length is x units.
To determine the opposite side's length, we determine the sin of the angle. To calculate the sin of an angle, we divide the opposite side's length by the hypotenuse's length.
[tex]sin\theta= \frac{oppositeside}{hypotenuse}, sin39=\frac{x}{30}.[/tex]
[tex]0.6293 = \frac{x}{30} , x = 18.879.[/tex]
GH measures 18.879 units. Rounding this off, we get 18.9 units.
Step 2:
Assume the side HI measures y units. According to Pythagoras' theorem,
[tex]30^{2}= 18.879^{2} +y^{2} , y^{2}=30^{2}-18.879^{2}.[/tex]
[tex]y^{2} = 543.5834, y = 23.314.[/tex]
So HI measures 23.314 units. Rounding this off, we get 23.3 units.
Step 3:
GHI is a triangle and all triangles have a total angle of 180°.
[tex]\begin{aligned}&\angle G^{\circ}+\angle H^{\circ}+\angle I^{\circ}=180^{\circ},\\&\angle G^{\circ}+90^{\circ}+39^{\circ}=180^{\circ},\\&\angle G^{\circ}=180^{\circ}-129^{\circ}=51^{\circ}.\end{aligned}[/tex]
So ∠G° measures 51°.
