3 years ago

A train travels 82 kilometers in 2 hours, and then 83 kilometers in 2 hours. What is its average speed?

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

41.25 kilometers per hour.

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The length of the hypotenuse of a right triangle is 20 feet. The tangent of one of the acute angles, angle 0, is 1.42. What is t

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Answer:

16.4 feet.

Step-by-step explanation:

We have been given that the length of the hypotenuse of a right triangle is 20 feet. The tangent of one of the acute angles, angle $\theta$ , is 1.42. We are asked to find the length of the side opposite angle $\theta$ .

We can represent our given information in an equation as:

$\text{tan}(\theta)=1.42$

Now, we will use arctan to solve for theta as:

$\theta=\text{tan}^{-1}(1.42)$

$\theta=54.85^{\circ}$

Now, we will use sine to solve for opposite side as sine relates opposite side of right triangle with hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{hypotenuse}}$

$\text{sin}(54.85^{\circ})=\frac{\text{Opposite}}{20}$

$20\cdot \text{sin}(54.85^{\circ})=\text{Opposite}$

$20\cdot 0.81764=\text{Opposite}$

$\text{Opposite}=20\cdot 0.81764$

$\text{Opposite}=16.3528$

$\text{Opposite}=16.4$

Therefore, the opposite side to angle theta is 16.4 feet.

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Everyone would get 0.6 oranges.

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