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n200080 [17]
3 years ago
13

Thomas decides to use the method of proportions and similar

Mathematics
2 answers:
Debora [2.8K]3 years ago
7 0

Answer:

The lamppost is 30 ft tall.

Step-by-step explanation:

You need to draw a diagram of the problem. Refer to attachment.

Now you need to convert the measurements that are in feet to in. The 1 foot ruler is now 12 in. and the 5 foot post's shadow is now 60 in.

The next step is to create a proportion between both angles. \frac{x}{1} =\frac{60}{2}

x over 1 is simplified to x and 60 divided by 2 is just 30. So the lamppost is 30 ft tall.

Hope that helped. :)

KATRIN_1 [288]3 years ago
4 0
I’m pretty sure it’s C
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Here is a diagram showing triangle ABC and some transformations of triangle ABC .On the left side of the diagram, triangle ABC h
Juli2301 [7.4K]

Answer:

1. For quadrilateral ABCD:

AB = AD = 2.7, BC = DC = 3.2, and AC = 3.168

<BAC = <DAC 65.5^{o}, <ABC = <ADC = 64.3^{o}, and <ACB = <ACD = 50.2^{o}

2. For quadrilateral ABCE:

AB = EC = 2.7, BC = AE = 3.2, and AC = 3.168

<BAC = <ACE 65.5^{o}, <ABC = <AEC = 64.3^{o}, and <ACB = <EAC = 50.2^{o}

Step-by-step explanation:

Applying the Cosine rule to triangle ABC,

/AC/^{2} = /AB/^{2} + /BC/^{2} - 2/AB/ x /BC/ Cos B

          = 2.7^{2} + 3.2^{2} - 2 x 2.7 x 3.2 Cos 64.3

         = 7.29 + 10.24 - 17.28 x 0.4337

         = 17.53 - 7.49434

         = 10.03566

AC = \sqrt{10.03566}

         = 3.168

Applying the Sine rule,

\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C}

So that:

\frac{3.2}{Sin A} = \frac{3.168}{Sin 643.^{o} }

\frac{3.2}{Sin A} = \frac{3.168}{0.9011}

Sin A = \frac{3.2 * 0.9011}{3.168}

         = \frac{2.88352}{3.168}

         = 0.9102

⇒ A = Sin^{-1} 0.9102

       = 65.5^{o}

But sum of angles in a triangle is 180^{o}, so that;

A + B + C = 180^{o}

65.5 + 64.3 + C = 180^{o}

129.8 + C    = 180^{o}

C  = 180^{o}  - 129.8

C = 50.2^{o}

1. For quadrilateral ABCD:

AB = AD = 2.7, BC = DC = 3.2, and AC = 3.168

<BAC = <DAC 65.5^{o}, <ABC = <ADC = 64.3^{o}, and <ACB = <ACD = 50.2^{o}

2. For quadrilateral ABCE:

AB = EC = 2.7, BC = AE = 3.2, and AC = 3.168

<BAC = <ACE 65.5^{o}, <ABC = <AEC = 64.3^{o}, and <ACB = <EAC = 50.2^{o}

7 0
3 years ago
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