Answer:
Option A is correct.
The length of g = 5.8 units.
Step-by-step explanation:
In triangle FGH
Given: \(m\angle F = 65^{\circ}\) and \(m\angle G = #5^{\circ}\)
As we know,
The sum of measures of the three angles of any triangle is 180 degree.
In triangle FGH
\(m\angle F+m\angle G+ m\angle H=180^{\circ}\)
Substitute the given values of angle F and angle G we get
\(65^{\circ}+35^{\circ}+ m\angle H=180^{\circ}\)
or
\(100^{\circ}+ m \angle H = 180^{\circ}\)
Simplify:
\(m\angle H = 80^{\circ}\)
To find the length of g;
Use sine law: Sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.
In ΔFGH as shown below in figure
By sine law we have;
\(\frac{\sin H}{h} = \frac{\sin G}{g}\)
Now, substitute the values angle H = 80°, angle G = 35° and h =10 units we have;
\(\frac{\sin 80}{10} = \frac{\sin 35}{g}\)
or
\(\frac{0.984808}{10}=\frac{0.573576}{g}\)
we can write this as;
\(g = \frac{0.573576 \times 10}{0.984808} =\frac{5.73576}{0.984808}\)
Simplify:
g = 5.82424188 ≈ 5.8 units.
Therefore, the length of g is, 5.8 units
