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dybincka [34]
3 years ago
13

Corey spies a bald eagle in a tall tree. He estimates the height of the tree to be 60 feet and the angle of elevation to the bir

d from where he stands to be 64°. The leaves on the tree make it difficult for Corey to watch the bird, so he takes many steps away from the tree to get a better view. He now estimates his angle of elevation to be 37°.
How many feet did Corey step back to gain a better view of the bird? Round your answer to the nearest hundredth of a foot.
Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

Corey stepped back 59.71 feet

Step-by-step explanation:

Right Triangles

They are a special type of triangle where one of its internal angles is 90°. The basic trigonometric equations stand in this type of triangles. If x is the adjacent leg of a given angle , and y is the opposite leg to the same angle, then :

tan0= \frac{y}{x}

We can solve for x to get

x = \frac{y}{tan0}

Corey estimates the height of the tree to be 80 feet. This means we know y=80 and . Let's find the horizontal distance at which Corey is looking at the bald eagle:

x1 =\frac{80}{tan68}

x1 = 32.32 feet

Now Corey moves back to watch the very same tree at an elevation angle of 41°. The tree has the same height, so

x2 =\frac{80}{tan41}

x2= 93.03 feet

Now we can know the distance Corey walked back by subtracting both distances

<em>correy stepped back 59.71 feet</em>

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Alika [10]

Answer:

c = 4

Step-by-step explanation:

In a perfect square trinomial, the following relationship is true:

(x+y)^2=x^2+2xy+y^2

In order for the given expression to be a perfect square trinomial:

x^2=x^2\\4x=2xy\\c=y^2

Solving for 'c':

4x=2xy\\y=2\\c=y^2=2^2\\c=4

Therefore, c must be equal to 4.

6 0
3 years ago
A cone has a base diameter of 20 centimeters. Its height is 30 centimeters. Calculate the volume in cubic centimeters to the nea
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Answer:

The volume of the cone is 3140cm³

Step-by-step explanation:

Volume of come = 1/3 × πr²h

r = diameter/2 = 20/2 = 10cm

h = 30cm

π = 22/7

Volume = 1/3 × 22/7 × 10² × 30

Volume = 1/3 × 22/7 × 100 × 30

Volume = 3142.86cm³

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3 years ago
19 photos are taken during school and 24 are taken after school. What fraction of photos were taken after school
yarga [219]
19 + 24= 43

\frac{24}{43}
4 0
3 years ago
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Andrea is painting a ceramic plate with a diameter of 12 inches. She wants to paint a thin blue line around the edge of the plat
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Answer:

37.7 inches

Step-by-step explanation:

She wants to paint the line along the circumference of the plate.

The plate is circular; the circumference of a circle is given as:

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where D = diameter

The diameter of the plate is 12 inches, therefore:

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The line will be 37.7 inches long.

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I need help ASAP <br> 120&gt;10n+20
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Answer:n = 10 can make the inequality true

Step-by-step explanation:

The given inequality is

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If we substitute n = 10 into the right hand side of the given inequality, it would result to 120.

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4 years ago
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