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22.03.2020 •
Mathematics
Find the missing length QG. Round answer to nearest tenth.
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Ответ:
The answer to your question is QG = 55.8 ft
Step-by-step explanation:
Data
QG = x
Process
1.- Find T
The sum of the internal angles in a triangle equals 180°
G + Q + T = 180
-Solve for T
T = 180 - G - Q
- Substitution
T = 180 - 41 - 67
-Simplification
T = 72°
2.- Use the law of sines to find QG
QG / sin T = GT / sin Q
-Solve for QG
QG = GT sinT / sin Q
-Substitution
QG = 54 sin 72 / sin 67
- Simplification
QG = 54 (0.951)/0.921
-Result
QG = 55.8 ft
Ответ:
Step-by-step explanation:
Considering the given triangle QGT, to determine QG, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes
QG/SinT = GT/SinQ = QT/SinG
The sum of the angles in a triangle is 180°. It means that
T = 180 - (41 + 67) = 72°
Therefore
QG/Sin72 = 54/Sin 67
Cross multiplying, it becomes
QGSin67 = 54Sin72
0.921QG = 54 × 0.951
0.921QG = 51.354
QG = 51.354/0.921
QG = 55.8 ft
Ответ: