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QveST [7]
3 years ago
6

Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°.

Mathematics
1 answer:
denis23 [38]3 years ago
3 0

Answer:

\boxed {\boxed {\sf About \ 28.36 \ meters }}

Step-by-step explanation:

Assuming the tree is perpendicular to the ground, we can use the right triangle trigonometric ratios to find the tree's height.

  • sin(θ)= opposite/hypotenuse
  • cos(θ)= adjacent/hypotenuse
  • tan(θ)= opposite/adjacent

Now, let's draw a diagram. We know Aiko is 5 meters from the base of the tree. From there, the angle to the top of the tree is 80 degrees. We are looking for x, the tree's height. The diagram attached is not to scale.

We base the sides off of the angle. x is opposite of 80 degrees and 5 is adjacent. Therefore we must use tangent.

tan(\Theta)=\frac{opposite}{adjacent}

  • opposite=x
  • adjacent=5 m
  • θ=80

Substitute in the known variables.

tan(80)=\frac{x}{5 \ m }

We want to find x, the height of the tree. Therefore we need to isolate that variable.

x is being divided and the inverse operation is multiplication. Multiply both sides of the equation by 5 meters.

5 \ m* tan(80)=\frac{x}{5 \ m }* 5 \ m

5 \ m* tan(80)=x

5 \ m *5.67128182=x

28.3564091 \ m = x

The question asks for an approximation, so let's round to the nearest hundredth.

The 6 in the thousandth place tells us to round the 5 to a 6.

28.36 \ m \approx x

The tree is about <u>28.36 meters tall.</u>

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Answer:

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Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
A 40% sugar solution is added to an 85% sugar solution to create 1800 mL of a 60% solution. How much of each solution is used? (
denis-greek [22]

Answer:

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

Step-by-step explanation:

Let the

Number of ml of 40% sugar = x

Number of ml of 85% sugar used = y

From the above question, our system of equations is given as:

x + y = 1800mL ....... Equation 1

x = 1800 - y

40% × x + 85% × y = 60% × 1800mL

0.4x + 0.85y = 1080.... Equation 2

We substitute 1800 - y for x in Equation 2

0.4(1800 - y) + 0.85y = 1080

720 - 0.4y + 0.85y = 1080

- 0.4y + 0.85y = 1080 - 720

0.45y = 360

y = 360/0.45

y = 800mL

Solving for x

x = 1800 - y

x = 1800 - 800

x = 1000mL

Therefore,

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

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2 years ago
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nata0808 [166]
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Each marble bag sold by Yolanda's Marble Company contains 8 orange marbles for every 5 yellow marbles.
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Solve for b means, write in the form of b =...

Given

+ b = - 1 and this is the same as b = - 1.

That is because the plus sign has no real meaning here, so you can ignore it as if it was not there at all.

It so turns out you now have the answer!

7 0
3 years ago
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