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makvit [3.9K]
3 years ago
9

In ΔEFG, the measure of ∠G=90°, the measure of ∠E=20°, and GE = 75 feet. Find the length of EF to the nearest tenth of a foot.

Mathematics
1 answer:
LenKa [72]3 years ago
7 0

Answer:80 feet

Step-by-step explanation:

Sum of < in a triangle is 180°

<G + <E + <F=180°

90 + 20 + < F = 110

< F = 70°

Using sine rule

sin G\EF = sin F\EG

sin90°\EF = sin70°\75

EF = 75sin90°\sin70°

= 79.81

=80 to the nearest tenth feet.

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Answer:

A) ∠9 = ∠10 = ∠11 = ∠12  = 90°

∠2 = ∠3 = ∠5 = ∠8 = 135°

∠1 = ∠4 = ∠6 = ∠7 = 45°

B) 1. ∠4 and ∠1 -> vertical angles

2. ∠7 and ∠5 -> supplementary

3. ∠9 and ∠10 -> supplementary

Step-by-step explanation:

<u>Data</u>

  • ∠4 = 45°
  • ∠5 = 135°
  • ∠10 = ∠11

The following are vertical angles, so they are congruent:

∠1 ≅ ∠4

∠3 ≅ ∠2

∠11 ≅ ∠9

∠10 ≅ ∠12

∠7 ≅ ∠6

∠5 ≅ ∠8

From here and data, it is deduced that

∠11 ≅ ∠9 ≅ ∠10 ≅ ∠12

From the picture, the addition of them is equal to 360°, then:

∠11 + ∠9 + ∠10 + ∠12 = 360°

4*∠11 = 360°

∠11 = 360°/4

∠11 = 90° = ∠10 = ∠9 = ∠12

∠2 and ∠4 are supplementary, then:

∠2 + ∠4 = 180°

∠2 = 180° - 45°

∠2 = 135°

∠7 and ∠5 are supplementary, then:

∠7 + ∠5 = 180°

∠7 = 180° - 135°

∠7 = 45°

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