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IrinaVladis [17]
4 years ago
13

Consider the diagram showing the path Joel biked.

Mathematics
2 answers:
Galina-37 [17]4 years ago
8 0

Answer:

36

Step-by-step explanation:

Tems11 [23]4 years ago
4 0

Answer:

He would 36 miles all together.

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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What are expressions for MN and LN? Hint Construct the altitude from M to LN.
Nikitich [7]

The question is missing the figure. So, it is in the atachment.

Answer: MN = x\sqrt{2}  LN = \frac{x}{2}.(\sqrt{2} + \sqrt{6} )

Step-by-step explanation: The first figure in the attachment is the figure of the question. The second figure is a way to respond this question by tracing the altitude from M to LN as suggested. When an altitude is drawn, it forms a 90° angle with the base, as shown in the drawing. To determine the other angle, you have to remember that all internal angles of a triangle sums up to 180°.

For the triangle <u>on the left</u> of the altitude:

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For the triangle <u>on the right</u>:

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With the angles, use the Law of Sines, which is relates sides and angles, as follows:

\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}

For MN:

\frac{x}{sin(30)} = \frac{MN}{sin(45)}

MN = \frac{x.sen(45)}{sen(30)}

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For LN:

\frac{LN}{sen(105)} =\frac{x}{sin(30)}

LN = \frac{x.sin(105)}{sin(30)}

We can determine sin (105) as:

sin(105) = sin(45+60)

sin(105) = sin(45)cos(60) + cos(45)sin(60)

sin(105) = \frac{\sqrt{2} }{2}.\frac{1}{2} + \frac{\sqrt{2} }{2}.\frac{\sqrt{3} }{2}

sin(105) = \frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}

LN = \frac{x.sin(105)}{sin(30)}

LN = x.(\frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}  ) .2

LN = \frac{x}{2}.(\sqrt{2} + \sqrt{6} )

The expressions for:

MN = x\sqrt{2}

LN = \frac{x}{2}.(\sqrt{2} + \sqrt{6} )

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