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frutty [35]
3 years ago
15

What is the angle of elevation of the sun when a pole 32.0 ft tall casts a shadow 45.0 ft long

Mathematics
1 answer:
Nostrana [21]3 years ago
8 0

As you can see in the first drawing, the vertical line represents the pole which is 32.0 ft long and the horizontal line represents the shadow casted by the pole which is 45.0 ft long. The angle θ, represents the angle of elevation of the sun.

We can solve this problem using trigonometric ratios, that is sine, cosine, and tangent. Remember SOH CAH TOA?

SOH

sin =  \frac{opposite}{hypotenuse}

CAH

cosine =  \frac{adjacent}{hypotenuse}

TOA

tan =  \frac{opposite}{adjacent}

In this case, we're going to use TOA since we are given the height of the pole which represents the line opposite the angle of elevation, and the length of the shadow of the pole which represents the line adjacent to the angle of elevation.

adjacent, a = 45.0

opposite, o = 32.0

So, to find the angle of elevation, refer to the second picture above.

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<u>Step-by-step explanation:</u>

Let x represent the 1st digit and y represent the 2nd digit. Then,

Eq 1: 2x + 3y = 9   →    3(2x + 3y = 9)     →     6x + 9y = 27

Eq 2: 3x + 2y = 1   →   -2(3x + 2y = 1)     →     <u>-6x - 4y =  -2</u>

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Substitute y = 5 into either of the original equations to solve for x:

2x + 3y = 9

2x + 3(5) = 9

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Check (using the other original equation):

3x + 2y = 1

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4 0
3 years ago
If angle EOF = 26 and angle FOG = 38., then what is the measure of angle EOG? The diagram is not to scale.
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Answer:

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Step-by-step explanation:

We can have a diagram for this.

From the description in the question, we can see that the ray FO splits the angle into 2.

We can have the diagram as shown in the attachment;

So mathematically;

EOG = EOF + FOG

So EOG = 26 + 38

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Please check attachment for a diagram

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