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makkiz [27]
3 years ago
13

Find all the missing elements. NEED HELP PLZZZZ

Mathematics
1 answer:
IgorC [24]3 years ago
7 0

Answer:

  • B=42°
  • C=98°
  • c=10.7 units

Step-by-step explanation:

Given

  • Angle A = Ф = 40°
  • a=8
  • b=7

We know that trigonometric ratio as

  • sin Ф = opposite/hypotenuse
  • cos Ф = adjacent/hypotenuse
  • tan Ф = opposite/adjacent

as

sin A = sin 40 = opposite/hypotenuse

From the diagram, it is clear that the opposite of angle A is a=8 and the hypotenuse is 'c'.

also the angle

sin A = sin 40 = opposite/hypotenuse = a/c = 8/c

sin 40 = 8/c

c = 8/sin 40

c = 8/0.745

c = 10.7

so the value of c will be: 10.7 units

so

tan B = opposite/adjacent

         = b/a

         = 0.9

B=\tan ^{-1}\left(0.9\right)

   =42^{\circ \:}

Therefore, the value of B = 42^{\circ \:}

As the sum of the angles of triangle ABC is 180.

i.e.

A+B+C = 180

(40)° + (42)° + C = 180°

C = 180° - 40° - 42°

  = 98°

Therefore, the value of C = 98°

Hence,

  • B=42°
  • C=98°
  • c=10.7 units
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