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3 years ago

In ΔFGH, the measure of ∠H=90°, GF = 41, HG = 40, and FH = 9. What ratio represents the cosine of ∠F?

Mathematics

2 answers:

xxTIMURxx [149]3 years ago

6 0

Answer:

Cosine F = (40 / 41)

Step-by-step explanation:

Since it's a right angle triangle, we can use

SOHCAHTOA method.

Where CAH = cosine F = adjacent / hypotenus.

Opposite (FH) = 9

Adjacent (HG) = 40

Hypothenus(FG) = 41

Cosine F = adjacent / hypothenus

Cosine F = 40 / 41

Cosine F = 0.9756

F = cos⁻(0.9756)

F = 12.68°

See attached document for better illustration on the triangle.

Nuetrik [128]3 years ago

4 0

Answer:

9/41

Step-by-step explanation:

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2 years ago

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Dmitry [639]

Answer: the distance of the boat from the foot of the lighthouse is 290.5 feet.

Step-by-step explanation:

The right angle triangle ABC representing the scenario is shown in the attached photo.

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6 0

3 years ago

Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+

tekilochka [14]

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

$h(t) = -16t^{2} + 72t + 100$

How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

$h(t) = -16t^{2} + 72t + 100$

$-16t^{2} + 72t + 100 = 0$

Multiplying by (-1)

$16t^{2} - 72t - 100 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$16t^{2} - 72t - 100 = 0$

$a = 16, b = -72, c = -100$

$\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584$

$t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61$

$t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11$

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.

3 0

3 years ago

Can anyone show me the steps in order solve this problem

STatiana [176]

M∠A = 42° [isosceles triangle]

m∠B = 180 - 42 - 42 = 96° [in a triangle, the three interior angles always add to 180°]

m∠C = 180 - 96 - (x+12)
m∠C = 84 - x - 12
m∠C = 72 - x

2x+9 + 3x-1 + 72-x = 180
4x + 80 = 180
4x = 180 - 80
4x = 100
x = 100/4
x = 25

m∠C = 72 - x = 72 - 25 = 47°

I hope this helped

8 0

3 years ago