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aliina [53]
3 years ago
10

Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who

is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. If Jack's and John's eyes are 1.5 meters from the ground and the distance from Jack's eyes to the top of the tower is 50.64 meters, how far is John from the base of the tower? Round your answer to the nearest tenth.
A.
24.5 meters

B.
16.1 meters

C.
22.2 meters

D.
18.8 meters

Mathematics
1 answer:
zmey [24]3 years ago
8 0

Answer:

18.7939 m

Step-by-step explanation:

-Let x be the distance between John and clock tower.

-Let y be the vertical distance from the eyes of the two men  standing to the top of the clock tower.

#Taking the right triangle ACD:

\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 60\textdegree=\frac{y+1.5}{x}\\\\y=x \ Tan \ 60\textdegree -1.5

#Taking the right triangle ABD:

\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 40\textdegree=\frac{y+1.5}{x+20}\\\\y=(x+20)\ Tan \ 40\textdegree -1.5

#We equate the two yo solve for x and y;

(x+20)\ Tan \ 40\textdegree -1.5=x\ Tan \ 60\textdegree -1.5\\\\(x+20)\ Tan \ 40\textdegree=x\ Tan \ 60\textdegree\\\\0.8391x+16.7820=1.7321x\\\\x=18.7939

Hence, John's distance from the tower's base is 18.7939 m

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vladimir1956 [14]

9514 1404 393

Answer:

  ∠CAB = 28°

  ∠DAC = 64°

Step-by-step explanation:

What you do in each case is make use of the relationships you know about angles in a triangle and around parallel lines. You can also use the relationships you know about diagonals in a rectangle, and the triangles they create.

<u>Left</u>

Take advantage of the fact that ∆AEB is isosceles, so the angles at A and B in that triangle are the same. If we call that angle measure x, then we have the sum of angles in that triangle is ...

  x + x + ∠AEB = 180°

  2x = 180° -124° = 56°

  x = 28°

The measure of angle CAB is 28°.

__

<u>Right</u>

Sides AD and BC are parallel, so diagonal AC can be considered a transversal. The two angles we're concerned with are alternate interior angles, so are congruent.

  ∠BCA = ∠DAC = 64°

The measure of angle DAC is 64°.

(Another way to look at this is that triangles BCE and DAE are congruent isosceles triangles, so corresponding angles are congruent.)

8 0
3 years ago
At the end of summer all sandals are marked down by 70%. If a pair of sandals originally cost $19.50, how much will it cost at t
aleksley [76]
70 percent off 19.50 would mean getting a discount of 13.65, so the final price of the sandals by the end of the summer should be 5.85
5 0
3 years ago
Which classification describes AMNO with vertices M(2, -3), N(3, 1), and<br> 0(-3, 1)?
Sonja [21]

Answer:

Option D

Step-by-step explanation:

32). Given vertices of the triangle are M(2, -3), N(3, 1) and O(-3. 1).

Distance between two points (x_1,y_1) and (x_2,y_2) is given by the expression,

Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Distance between M(2, -3) and N(3, 1) will be,

MN = \sqrt{(3-2)^2+(1+3)^2}

      = \sqrt{1+16}

      = \sqrt{17}

Distance between M(2, -3) and O(-3, 1),

MO = \sqrt{(2+3)^2+(-3-1)^2}

      = \sqrt{25+16}

      = \sqrt{41}

Distance between N(3, 1) and O(-3, 1),

NO = \sqrt{(3+3)^2+(1-1)^2}

      = 6

Condition for right triangle,

c² = a² + b² [Here c is the longest side of the triangle]

By this property,

MO² = MN² + NO²

(\sqrt{41})^2=(\sqrt{17})^2+6^2

41 = 17 + 36

41 = 51

False.

Therefore, given triangle is not a right triangle.

Since, length of all sides are not equal, given triangle will be a scalene triangle.

Option D is the correct option.

5 0
3 years ago
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Karo-lina-s [1.5K]

Answer:

720

Step-by-step explanation:

50/8=6.25

4,500/6.25=720

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2 years ago
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ivann1987 [24]
The standard form would be y = 7x^2 - 42x + 67
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