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skad [1K]
3 years ago
15

The furthest angle of elevation to the top of the steeple was 20 degrees and the closest angle elevation to the church was 29 de

grees. Each person is 1.7 meters tall from his feet to his eyeballs. Find the measure of angle ACB. (Hint: Find measure of angle ABC first).
A) 151 degrees
B) 9 degrees
C) 171 degrees
D) 20 degrees

Mathematics
1 answer:
Otrada [13]3 years ago
7 0

The angle measure of ACB is 9 degrees

Answer: Option B

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

To find the solution to the given problem, first we need to look into the point B. It consists two angles and both of them are on a straight angle. So, this means that the sum of angle ABC and CBD is 180 degrees, that is

               \angle A B C+\angle C B D=180^{\circ}

We know that \angle C B D=29^{\circ}. Therefore

               \angle A B C+29^{\circ}=180^{\circ}

               \angle A B C=180^{\circ}-29^{\circ}=151^{\circ}

Now, in the triangle ABC, we know that all three angles must sum 180 degrees,

               \angle C A B+\angle A B C+\angle B C A=180^{\circ}

               20^{\circ}+151^{\circ}+\angle B C A=180^{\circ}

               \angle B C A=180^{\circ}-20^{\circ}-151^{\circ}=9^{\circ}=\angle A C B

Therefore, the angle ACB is 9 degrees.

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Complete Question

Given quadrilateral EFGH with vertices at E(-4,8), F(8,4), G(5,-5) and H(-7,-1), prove using coordinate geometry that EFGH is a rectangle.

Answer:

Quadrilateral EFGH is a rectangle.l because:

EF = GH and FG = EH

Step-by-step explanation:

The formula for coordinate geometry is given as :

√(x2 - x1)² + (y2 - y1)² when we have coordinates: (x1, y1) and (x2 , y2)

For the quadrilateral EFGH with given coordinates above to be a rectangle,

EF = GH

FG = EH

Hence:

For side EF

E(-4,8), F(8,4)

= √(8 - (-4))² + (4 - 8)²

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= √144 + 16

= √160 units

For side FG

F(8,4), G(5,-5)

=√(5 - 8)² + (-5 - 4)²

= √-3² + -9²

= √9 + 81

= √90 units

For Side GH

G(5,-5) , H(-7,-1)

= √(-7 - 5)² + (-1 - (-5))²

= √-12² + 4²

= √144 + 16

= √160 units

For side EH

E(-4,8), H(-7,-1)

= √(-7 -(-4))² +(-1 - 8)²

= √-3² + -9²

= √9 + 81

= √90 units

From the above calculation, we can see that truly,

EF = GH

FG = EH

Therefore, quadrilateral EFGH is a rectangle.

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