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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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<em>Proof in the explanation</em>

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<u>Trigonometric Equalities</u>

Those are expressions involving trigonometric functions which must be proven, generally working on only one side of the equality

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\displaystyle arccos\ \sqrt{\frac{2}{3}}-arccos\left(\frac{1+\sqrt{6}}{2\sqrt{3}}\right)=\frac{\pi}{6}  

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\displaystyle x=arccos\ \frac{\sqrt{6}}{3}}=>\ cos\ x= \frac{\sqrt{6}}{3}}

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\displaystyle y=arccos\ \frac{1+\sqrt{6}}{2\sqrt{3}}=>cos\ y=\frac{1+\sqrt{6}}{2\sqrt{3}}=\frac{\sqrt{3}+3\sqrt{2}}{6}

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\displaystyle cos(x-y)=\frac{9\sqrt{3}}{18}=\frac{\sqrt{3}}{2}=cos\ \pi/6

Thus, proven  

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