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Levart [38]
3 years ago
8

Consider the diagram showing the path Joel biked. Joel biked 9 miles east and then 12 miles north. If he biked back to his start

ing point using the most direct route, how many miles would he ride all together? Joel’s starting point is x

Mathematics
2 answers:
natulia [17]3 years ago
7 0

Using the Pythagorean theorem:

The direct distance back would be:

√(9^2 + 12^2)

√(81 + 144)

√225

15 miles

The total miles would be the sum of the 3 sides:

15 + 9 +12 = 36 total miles.

Andrej [43]3 years ago
5 0

Answer:

36 miles

Step-by-step explanation:

Consider the diagram showing the path Joel biked. Joel biked 9 miles east and then 12 miles north. If he biked back to his starting point using the most direct route, he would have ride 36 miles all together. Joel’s starting point is x.

In order to solve this, we must use the Pythagorean theorem.

The amount of miles would be found by adding the 3 sides together to find the sum or answer.

15 + 9 + 12 = 36 miles

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We have been given that \text{sin}(A)=\frac{12}{13} and angle A is in quadrant 1. We are asked to find the exact value of \text{cot}(A) in simplest radical form.

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\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}

Now we will find adjacent side using Pythagoras theorem as:

\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2

\text{Adjacent}^2=13^2-12^2

\text{Adjacent}^2=169-144

\text{Adjacent}^2=25

Let us take positive square root on both sides:

\sqrt{\text{Adjacent}^2}=\sqrt{25}  

\text{Adjacent}=5

Therefore, adjacent side of angle A is 5 units.

\text{cot}(A)=\frac{5}{12}

Therefore, the exact value of cot A is \frac{5}{12}.

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6. A line that passes through the point (–1, 3) has a slope of 2. Find another point on the line. A. (0, 5) B. (–3, 2) C. (1, 4)
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Step-by-step explanation:

Given,

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