Question

How can I do this ???​

Answer 1

Answer:

The triangle EFG can be constructed with the following specifications: $EF = 8\,cm$, $FG = 7\,cm$, $EG = 12\,cm$, $E \approx 34.093^{\circ}$, $F \approx 106.068^{\circ}$, $G \approx 39.838^{\circ}$.

Step-by-step explanation:

A triangle is formed by either knowing the lengths of its three sides or knowing two angles and the length of a side or knowing a angle and the lengths of two sides. By Geometry, we know that sum of internal angles in triangles equals 180°. In order to construct this triangle, we need to know the measures of angles E, F and G by means of the Law of Cosine:

Angle E

$E = \cos^{-1}\left[\frac{(7\,cm)^{2}-(12\,cm)^{2}-(8\,cm)^{2}}{-2\cdot (12\,cm)\cdot (8\,cm)} \right]$

$E \approx 34.093^{\circ}$

Angle F

$F = \cos^{-1}\left[\frac{(12\,cm)^{2} - (8\,cm)^{2} - (7\,cm)^{2}}{-2\cdot (8\,cm)\cdot (7\,cm)} \right]$

$F \approx 106.068^{\circ}$

Angle G

$G = \cos^{-1}\left[\frac{(8\,cm)^{2}-(12\,cm)^{2}-(7\,cm)^{2}}{-2\cdot (12\,cm)\cdot (7\,cm)} \right]$

$G \approx 39.838^{\circ}$

The triangle EFG can be constructed with the following specifications: $EF = 8\,cm$, $FG = 7\,cm$, $EG = 12\,cm$, $E \approx 34.093^{\circ}$, $F \approx 106.068^{\circ}$, $G \approx 39.838^{\circ}$.