4 years ago

In ΔEFG, the measure of ∠G=90°, the measure of ∠F=23°, and FG = 31 feet. Find the length of GE to the nearest tenth of a foot.

Mathematics

1 answer:

alexira [117]4 years ago

6 0

Answer:

x=13.1587≈13.2 feet

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Angle α lies in quadrant II , and tan α = <img src="https://tex.z-dn.net/?f=-%5Cfrac%7B12%7D%7B5%7D" id="TexFormula1" title="-\f

Hunter-Best [27]

Since $\alpha$ lies in quadrant II and $\beta$ lies in quadrant IV, we expect $\sin\alpha>0$ , $\cos\alpha$ , and $\sin\beta$ .

Recall the Pythagorean identities,

$\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x$

It follows that

$\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}$

$\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}$

$\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45$

Recall the angle sum identity for sine:

$\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$

So we have

$\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}$

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3 years ago

Whats the inverse function of d(t)=70t

Charra [1.4K]

Answer:

d^-1(t)=t/70

Step-by-step explanation:

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3 years ago

Suppose that to make the golf team you need to score no more than 74 on average over 5 games. If you scored 77, 71, 77, and 67 i

lord [1]

A score of 78

77+71+77+67+78=370
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3 years ago

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Ricardo had 2 case of video game with the same number of games in each case .he gives 4 games to his brother.Ricardo has 10 game

Drupady [299]

Answer:

Step-by-step explanation:

The total number of video games he had to begin with is 4+10=14.

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3 years ago

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F(x) is another way to say “y” so you could also write, y=2(x+6)-4, and it’s asking what does x equal if y is 6, so you substitute 6 for y.
6=2(x+6)-4
6=2x+12-4
6=2x+8
-2=2x
-1=x

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3 years ago