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zzz [600]
2 years ago
11

If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building?

Round the answer to the nearest tenth of a foot. 10. 3 ft 17. 6 ft 30. 2 ft 97. 2 ft.
Mathematics
1 answer:
elena55 [62]2 years ago
7 0

The closer Diana gets to the building, the smaller the angle becomes

Diana is 17.6 feet closer to the building

<h3>How to calculate the distance from the building</h3>

To calculate the distance between her and the building, we make use of the following tangent ratio

\tan(\theta) = \frac{h}{d}

Where:

  • \theta = 40^o
  • h represents the height of the building; h = 130
  • d represents the distance from the building

So, we have:

\tan(40) = \frac{130}{d}

Make d the subject

d = \frac{130}{\tan(40)}

Evaluate tan(40)

d = \frac{130}{0.8391}

d = 154.93

Initially, Diana is at a distance of 172.53.

The difference in both distance is:

\Delta d = 172.53 - 154.93

\Delta d = 17.6

Hence, Diana is 17.6 feet closer to the building

Read more about trigonometry ratios at:

brainly.com/question/4326804

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(It's the slope formula)

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then plug in... \frac{3-3}{2-10} =\frac{0}{-8} = 0

this line has a slope of 0


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6 0
3 years ago
Find the values of x, y, and z. The diagram is not to scale.
rosijanka [135]

Answer:

x= 81°, z= 99°, y°=68°

Step-by-step explanation:

considering the part of the triangle where 36° , 63° and x° is located as ΔABC.

to find the measure of x we use angle sum property.

We know that the sum of the angles of a triangle is always 180°. Therefore, if we know the two angles of a triangle, and we need to find its third angle, we use the angle sum property. We add the two known angles and subtract their sum from 180° to get the measure of the third angle.

so,

∠A + ∠B +∠C = 180°

36° + 63° + x° = 180°

99° + x° = 180°

x° = 180 - 99

x° = 81°

When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.

x° + z° = 180°

81° + z = 180°

z= 180 - 81

z= 99°

considering the next part of the triangle where 13° , z° and y° is located as ΔACD

to find the measure of y we use angle sum property.

∠A + ∠C + ∠D = 180°

13° + z° + y° = 180°

13°+99°+y°= 180°

112°+ y° = 180°

y°= 180- 112

y° = 68°

5 0
2 years ago
Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript neg
Darina [25.2K]

By using exponent properties, we will get the simplified expression:

x^{-1}*y^{1/2}*z^2

<h3>How to simplify the given expression?</h3>

Here we have the expression:

(x^{1/2}*y^{-1/4}*z)^{-2}

Remember the exponent properties:

(a^n)^m = a^{n*m}

And:

(a*b)^n = (a^n)*(b^n)

So using these two properties, we can rewrite:

(x^{1/2})^{-2}*(y^{-1/4})^{-2}*(z)^{-2}\\\\(x^{-2*1/2})*(y^{-2*-1/4})*(z^{-2}})\\\\x^{-1}*y^{1/2}*z^2

So we conclude that the completely simplified expression is:

x^{-1}*y^{1/2}*z^2

If you want to learn more about exponents:

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8 0
2 years ago
2, 4, 13, 49, 193,
PolarNik [594]

If we begin with the first term, 2, mult. it by 4 and then subtract 3, we get 5 (not 4, as shown).

If we begin with 4, mult. it by 4 and then subtract 3, we get 13. This agrees with the terms of the given sequence.

If we begin with 13, mult. it by 4 and then subtract 3, we get 49. This agrees with the terms of the given sequence.

Remove the first term, 2, and then the remaining terms follow the given procedure for finding terms.


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shtirl [24]
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