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nata0808 [166]
3 years ago
9

The blue lake trail is 11 3/8 miles long. Gemma has hiked 2 1/3 miles each hour for 3 hours. How far is she from the end of the

trail?
Mathematics
1 answer:
sergeinik [125]3 years ago
4 0

Answer:

4\frac{3}{8}miles

Step-by-step explanation:

Given that Gemma has hiked 2 1/3 mile each hour for a total of 3 hours, you can multiply her rate by her time to find the total distance:

d = rt or d = 2 1/3(3)

2\frac{1}{3}=\frac{7}{3}

Multiply: \frac{7}{3}*\frac{3}{1}=7miles

Now, that the total length of the trail, 11 3/8 miles, and subtract the distance that Gemma has gone already:

11 3/8 - 7 = 4\frac{3}{8}miles

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Step-by-step explanation:

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              C

              ↓

               ↑

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If this right angle triangle is considered, length bc is the hypotenuse and length ac is the opposite side of angle B.

The length of ac is calculated as follows;

tan \ B = \frac{opposite \ side}{adjacent \ side} \\\\tan \ B = \frac{ac}{ab} \\\\ac = ab \ \times \ tan \ B\\\\ac = 16\sqrt{3} \ \times \frac{\sqrt{3} }{3} \\\\ac = \frac{16 \sqrt{9} }{3} \\\\ac = \frac{16 \times 3}{3} \\\\ac = 16

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