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1 answer:
Answer:
Considerations:
Also,
A positive number divided by a positive number results in a positive quotient, and its opposite is always negative.
The fraction can be described as a positive number divided by a negative number, which always result in a negative quotient.
The fractions have same value, so Liam is correct.
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The complete question asks "If mDB <span>= 60° and PE = 3, then PB =?"
The correct answer is C) PB = 6.
Explanation:
See the attached picture for reference.
We know
</span>∠DBP = 60°
PB ≡ PD because they are both radius of the circunference, which means that ΔPDB is an isosceles triangle of base DB.
As a consequence, ∠DBP ≡ <span>∠PDB = 60°.
But then </span>∠DPB = 180 - 60 - 60 = 60°.
An isosceles triangles with all the angles measuring 60° is an equilateral triangle.
In an equilateral triangle, the height (DE) cuts into to equl parts the side PB, which means that PE = (1/2) PB
We know PE = 3, therefore
PB = 2 × PE
= 2 × 3
= 6
Hence, PB = 6.
The correct answer is C) PB = 6.
Explanation:
See the attached picture for reference.
We know
</span>∠DBP = 60°
PB ≡ PD because they are both radius of the circunference, which means that ΔPDB is an isosceles triangle of base DB.
As a consequence, ∠DBP ≡ <span>∠PDB = 60°.
But then </span>∠DPB = 180 - 60 - 60 = 60°.
An isosceles triangles with all the angles measuring 60° is an equilateral triangle.
In an equilateral triangle, the height (DE) cuts into to equl parts the side PB, which means that PE = (1/2) PB
We know PE = 3, therefore
PB = 2 × PE
= 2 × 3
= 6
Hence, PB = 6.
Correct response:
- The height of equilateral triangle ΔABC is <u>12 inches</u>
Given:
ΔABC is a equilateral triangle
Point <em>D</em> is on side BC
Point <em>R</em> is on side AB
Point <em>T</em> is on side AC
DR = 4 inches
DT = 8 inches
Required:
The height in inches of equilateral triangle ΔABC.
Solution:
By sine rule, we have;
Therefore;
4·sin(60° - θ) = 8·sin(θ)
- sin(A - B) = sin(A)·cos(B) - cos(A)·sin(B)
Therefore;
4·(sin(60°)·cosθ - cos(60°)·sin(θ)) = 8·sin(θ)
Dividing by sin(θ) gives;
4·(sin(60°)·cot(θ) - cos(60°)) = 8
sin(60°)·cot(θ) - cos(60°) = 8 ÷ 4 = 2
Multiplying by 2 gives;
√3·cot(θ) - 1 = 4
√3·cot(θ) = 4 + 1 = 5
Therefore;
Length of a side of the equilateral triangle,<em> L</em>, is therefore;
Therefore;
Height, <em>h</em>, of the equilateral triangle ΔABC is, h = L × sin(60°)
Therefore;
- The height of the equilateral triangle, h = <u>12 inches</u>
Learn more about trigonometric ratios here:
