Angelique draws triangle GHK. If A.1.2 or 5.7 B.2.2 or 4.7 C.4.7 D.5.7

Mathematics

2 answers:

makvit [3.9K]2 years ago

7 0

The correct question in the attached figure

we know that

applying the law of sines
g/sinG=k/sinK

g=3 units
G=30°
k=4 units
K=?
so
g/sinG=k/sinK------> g*sinK=k*sinG-----> sinK=k*sinG/g
sinK=4*sin 30°/3-----> 2/3
K=arc sin(2/3)-------> K=41.81°

case 1)
for angle K=41.81°
the sum of the angles (H +G+K)=180°
H=180-(G+K)------> 180-(30+41.81)--------> H=108.19°

h/sinH=g/sinG-------> h=g*sinH/sinG------> h=3*sin 108.19°/sin 30°
h=5.70 units

case 2)
for angle K=180°-41.81°---------> K=138.19°
the sum of the angles (H +G+K)=180°
H=180-(G+K)------> 180-(30+138.19)--------> H=11.81°

h/sinH=g/sinG-------> h=g*sinH/sinG------> h=3*sin 11.81°/sin 30°
h=1.2 units

therefore

the answer is the option
A. 1.2 or 5.7