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kvasek [131]
3 years ago
15

Hayden likes building radio controlled sailboats with her father. One of the sails shaped like a tight triangle has side lengths

measuring 6 inches 8 inches and 10 inches. To log her activity hayden creates and collects drawings of all the boats she and her father built together. Using the scale factor of 1/4 create a scale drawing of the sail

Mathematics
1 answer:
disa [49]3 years ago
6 0

Answer:

the scaled sail has lengths 1.5 inches, 2 inches, and 2.5 inches. the diagram is attached.

Step-by-step explanation:

a scale factor of 1/4 means that the lengths of each side of the sail will be reduced by 0ne-forth (0.6) its original length. Therefore the lengths of the scale drawing before and after scaling are:

6 inches = 6 × 1/4 = 6 × 0.25 = 1.5 inches

8 inches = 7 × 0.25 = 2 inches

10 inches = 10 × 0.25 = 2.5 inches.

Therefore the scaled sail has lengths 1.5 inches, 2 inches, and 2.5 inches as shown in the diagram attached.

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Answer:

<em>A.</em>

<em>The student made an error in step 3 because a is positive in Quadrant IV; therefore, </em>

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Step-by-step explanation:

Given

P\ (a,b)

r = \± \sqrt{(a)^2 + (b)^2}

cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}

Required

Where and which error did the student make

Given that the angle is in the 4th quadrant;

The value of r is positive, a is positive but b is negative;

Hence;

r = \sqrt{(a)^2 + (b)^2}

Since a belongs to the x axis and b belongs to the y axis;

cos\theta is calculated as thus

cos\theta = \frac{a}{r}

Substitute r = \sqrt{(a)^2 + (b)^2}

cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}

cos\theta = \frac{a}{\sqrt{a^2 + b^2}}

Rationalize the denominator

cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}

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<em>The student's mistake is that a is positive in quadrant iv and his error is in step 3</em>

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