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Kay [80]
3 years ago
15

In ΔUVW, w = 9 cm, v = 2.2 cm and ∠V=136°. Find all possible values of ∠W, to the nearest 10th of a degree.

Mathematics
1 answer:
Alja [10]3 years ago
3 0

Complete Question

In ΔUVW, w = 9 cm, v = 22 cm and ∠V=136°. Find all possible values of ∠W, to the nearest 10th of a degree.

Answer:

16.5°

Step-by-step explanation:

In ΔUVW, w = 9 cm, v = 22 cm and ∠V=136°. Find all possible values of ∠W, to the nearest 10th of a degree.

We solve using Sine rule formula

a/sin A = b/sin B

We are solving for angle W

∠V=136°

Hence:

22 /sin 136 = 9 /sin W

Cross Multiply

22 × sin W = sin 136 × 9

sin W = sin 136 × 9/22

W = arc sin [sin 136 × 9/2.2]

W = 16.50975°

W = 16.5°

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A rectangular billboard image is 5 ft wide and 4 ft high. If the available billboard space is 25 ft by 15 ft, what are the dimen
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Answer:

18¾ ft × 15 ft

Step-by-step explanation:

The dimensions of the billboard are 25 ft by 15 ft.

The dimensions of the image are 5 ft by 4 ft  

Case 1.<em> Expand the length of the image to 25 ft. </em>

We have multiplied the length by five, so we must multiply the width by five.

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<em>Case 2. </em><em>Expand the width of the image to 15 ft. </em>

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5 0
3 years ago
Con
mr Goodwill [35]

Answer:

The coordinates of E are E(x,y) = \left(\frac{9}{2}, 0 \right).

Step-by-step explanation:

The triangle ABC represents a right triangle as both sides AB and AC are orthogonal to each other. The side AB is in the y axis, whereas the side AC is in the x axis. The triangle is dilated with respect to the origin, in which point A is set.

Vectorially speaking, dilation is defined by the following operation:

P'(x,y) = O(x,y) + k\cdot [P(x,y) - O(x,y)] (1)

Where:

O(x,y) - Point of reference.

P(x,y) - Original point.

P'(x,y) - Dilated point.

k - Dilation factor.

By applying this operation, point B becomes point D:

B(x,y) = (0,4), D(x,y) = (0,6)

D(x,y) = (0,0) + k\cdot [(0,4)- (0,0)]

D(x,y) = (0,0) + k\cdot (0,4)

(0,6) = (0,0) +(0,4\cdot k)

(0, 6) = (0,4\cdot k)

k = \frac{3}{2}

Lastly, we transform point C into point E by applying the same operation: C(x,y) = (3, 0), O(x,y) = (0,0) and k = \frac{3}{2}

E(x,y) = (0,0) + \frac{3}{2}\cdot [(3,0)-(0,0)]

E(x,y) = \left(\frac{9}{2}, 0 \right)

The coordinates of E are E(x,y) = \left(\frac{9}{2}, 0 \right).

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Step-by-step explanation:

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