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Allisa [31]
2 years ago
9

The figure below shows triangle wooden frame ABC. The side AD of the frame has rotted and needs to be replaced. What is the le

ngth of the wood that is needed to replace AD?
4.2
5.7
2.5
1.3

Mathematics
1 answer:
Mamont248 [21]2 years ago
3 0

Answer:

AD = 4.2 in

Step-by-step explanation:

We'll begin by calculating the length AB. This can be obtained as follow:

Angle C = 15 + 30 = 45°

Adjacent = BC = 10 in

Opposite = AB =?

The length AB can be obtained by using the tan ratio as illustrated below:

Tan C = Opposite / Adjacent

Tan 45 = AB / 10

1 = AB / 10

Cross multiply

AB = 1 × 10

AB = 10 in

Next, we shall determine the length BD. This can be obtained as follow:

Angle C = 30°

Adjacent = BC = 10 in

Opposite = BD =?

The length BD can be obtained by using the tan ratio as illustrated below:

Tan C = Opposite / Adjacent

Tan 30 = BD / 10

0.5774 = BD / 10

Cross multiply

BD = 0.5774 × 10

BD = 5.8 in

Finally, we shall determine length AD. This can be obtained as follow:

AB = 10 in

BD = 5.8 in

AD =?

AB = BD + AD

10 = 5.8 + AD

Collect like terms

10 – 5.8 = AD

4.2 = AD

AD = 4.2 in

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Read 2 more answers
Mike bought five items for lunch that cost a total of $4.55. Hot dogs cost $1.10 each and cookies cost $0.75 each. Which of thes
Setler79 [48]

Answer:

1.1h+0.75c=4.55---------------1

h+c=5--------------2

Step-by-step explanation:

Step one:

given data

total lunch items= 5

let hot dogs be h

and cookies be c

cost of hot dogs = $1.10

cost of cookies = $0.75

total cost = $4.55

Step two:

The linear model for the total cost is given as

4.55=1.1h+0.75c---------------1

and the model for the number of items is

h+c=5--------------2

The systems of the equation for the situation is

1.1h+0.75c=4.55---------------1

h+c=5--------------2

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Answer:

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Step-by-step explanation:

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