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fiasKO [112]
3 years ago
10

Triangle ABC has vertices at A(2,5), B(4,11) and C(-1,6). Determine the angles in this triangle.

Mathematics
1 answer:
ELEN [110]3 years ago
4 0

Answer:

The angles are

∠A = 90°, ∠B = 26.56°, ∠C = 63.43°

Step-by-step explanation:

We have that the angles of a vector are given as follows;

cos\left ( \theta   \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}

Whereby the vertices are represented as

A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),

AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) ,  BA = (-2, -6, 0)

BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)

AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)

θ₁ = AB·AC

a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0

Therefore, θ₁ = 90°

BA·BC = (-2)×(-5) + (-6)×(-5) = 40

{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |} = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72

cos(θ₂) = 40/44.72 = 0.894

cos⁻¹(0.894) =θ₂= 26.56°

CA·CB = 5×3 + 5×(-1) = 10

{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |} = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36

10/22.36 = 0.447

cos(θ₃) = 0.447

θ₃ = cos⁻¹(0.447) = 63.43°.

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Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new wall
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The relationship between the length & the width of the closet and the length of the wall is an illustration of a linear equation.

  • <em>The equation for f(l) is: </em>f(l) = 1.5l<em>.</em>
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<em />

Given that:

l = 2w

Divide both sides by 2

w = 0.5l

<u>Equation of f(l)</u>

The sum of the length and the width is represented as: f(l).

So, we have:

f(l) = l + w

Substitute w = 0.5l

f(l) = l + 0.5l

f(l) = 1.5l

See attachment for the graph of f(l)

<u>The desired dimension</u>

From the question, we understand that the total length is 12m.

This means that:

f(l) = 12

So, we have:

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Recall that:

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w = 0.5 \times 8

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Hence, the desired length and width are 8m and 4m, respectively.

Read more about linear equations at:

brainly.com/question/2263981

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Given:

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Solution:

The reference image is attached below.

Joining mid-point M and N, we get mid-segment MN.

MN is parallel to RT.

Triangle mid-segment theorem:

If a segments joins the mid point of a two sides of triangle, then the segment is parallel to the third side and is half of that side.

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$\Rightarrow 2\times 18.4 =2\times \frac{1}{2} RT

$\Rightarrow 36.8=RT

The length of RT is 36.8.

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