Find all the missing parts to the triangle below
2 answers:
<h2>
Answer:</h2>
We have:
<h2>
Step-by-step explanation:</h2>
We are given angle F as:
m∠GF=87°
Now, g=28 and h=15 we are asked to find f.
Using the law of cosines we have:

which is approximately equal to 31 units
Hence, f=31 units
Also,

Hence, to the nearest degree we get:
m∠G=64°
Also, we know that the sum of all the angles of a triangle is 180°
Hence,
m∠F+m∠G+m∠H=180°
i.e.
87°+64+m∠H=180°
m∠H=29°
Use Law of Cosines g^2 = f^2 + h^2 -2fhCosG f^2 = g^2 + h^2 -2ghCosF h^2 = f^2 + g^2 -2fgCosH
f^2 = 28^2 + 15^2 -2*28*15Cos87 28^2 = 31^2 + 15^2 -2*31*15CosG
f^2 = 784 + 225 - 43.96 784 = 961+225 - 930CosG
f^2 = 965.0378 784 - 1186 = -930CosG
f = 31 -402 = -930CosG Divide by -930
.432258 = CosG
Cos^-1(.432258) = G
G = 64 degrees
Angle H = 180 - 64 - 87 = 29 degrees
Side f = 31 Angle F = 87 degrees
Side g = 28 Angle G = 64 degrees
Side h = 15 Angle H =29 degrees
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