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Fudgin [204]
2 years ago
8

PLEASE HELP ME!! A section of a highway is constructed with a 23% grade. What angle does the highway make with a horizontal line

? Round to the nearest hundredth of a degree.
m∠A ≈ 12.95°

m∠A ≈ 77.05°

m∠A ≈ 14.95°

m∠A ≈ 87.05°

Mathematics
1 answer:
lesantik [10]2 years ago
4 0

Answer: 77.05

Step-by-step explanation:    1) Draw a right triangle with these measures:

angle with the horizontal: 6 degress

horizontal segment: 5

height: x

2) Definition of tangent : tan(6°) = opposite leg / adjacent leg = x / 5 =>

3) Solve for

x = 5tan(6°) = 77.05

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Answer:

Option d is correct.

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SAS

Step-by-step explanation:

Given: JK \cong KL , NK \cong KM

In ΔNKJ and  ΔMLK

JK \cong KL and      [Side]                 {Given}

NK \cong KM      

Vertical angles states that the two lines intersect to make an X, angles on opposite sides of the X are called vertical angles.

i.e \angle NKJ and \angle MKL are vertical angles.

Also, vertical angles are congruent.

\angle NKJ \cong \angle MKL  [Angle]      [Vertical angles are congruent]

SAS(Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

then, by SAS postulates;

\triangle NKJ \cong \triangle MLK          Hence proved!

Therefore:

Statement                                                                      Reason

1.  JK \cong KL, NK \cong KM           Given

2.  \angle NKJ \cong \angle MKL                 Vertical angles are congruent

3. \triangle NKJ \cong \triangle MLK             SAS

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