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3 years ago

Find the missing side length of the triangie. 12 in. 35 in.

Mathematics

1 answer:

OlgaM077 [116]3 years ago

6 0

Answer:

Step-by-step explanation:

Right Scalene Triangle

Side a = 37

Side b = 12

Side c = 35

Angle ∠A = 90° = 1.5708 rad = π/2

Angle ∠B = 18.925° = 18°55'29" = 0.3303 rad

Angle ∠C = 71.075° = 71°4'31" = 1.2405 rad

C=71.075°B=18.925°A=90°b=12a=37c=35

Area = 210

Perimeter p = 84

Semiperimeter s = 42

Height ha = 11.35135

Height hb = 35

Height hc = 12

Median ma = 18.5

Median mb = 35.51056

Median mc = 21.2191

Inradius r = 5

Circumradius R = 18.5

Vertex coordinates: A[0, 0] B[35, 0] C[0, 12]

Centroid: [11.66667, 4]

Inscribed Circle Center: [5, 5]

Circumscribed Circle Center: [17.5, 6]

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Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

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$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

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squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

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$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

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$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

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