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vaieri [72.5K]
2 years ago
10

What is the length of the arc by a central angle of 85 degrees and a radius of 8cm to the nearest tenth of a cm?

Mathematics
2 answers:
Temka [501]2 years ago
7 0

Answer:

11.86824cm

Step-by-step explanation:

Amiraneli [1.4K]2 years ago
5 0

Answer:

11.86824cm

Step-by-step explanation:

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A statue is mounted on top of a 21 foot hill. From the base of the hill to where you are standing is 57feet and the statue subte
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Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

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\angle SPR=Angle subtended by the statue to where you are standing.

\angle x=\angle RPQ= which is unknown.

Let us begin solving now. The first step is to find the angle \angle x which can be found by using the following trigonometric ratio in \Delta PQR :

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Which gives \angle x to be:

\angle x=tan^{-1}(\frac{21}{57})\approx20.22^{0}

Now, we know that\angle x and \angle SPR can be added to give us the complete angle \angle SPQ in the right triangle \Delta SPQ.

We can again use the tan trigonometric ratio in \Delta SPQ to solve for the height of the statue, h.

This can be done as:

tan(\angle SPQ)=\frac{SQ}{PQ}

tan(7.1^0+20.22^0)=\frac{SR+RQ}{PQ}

tan(27.32^0)=\frac{h+21}{57}

\therefore h+21=57tan(27.32^0)

h\approx8.45 ft

Thus, the height of the statue is approximately, 8.45 feet.

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It is not a horizontal translation, this means that the triangle shifted left or right.

It is not a rotation about point A either, this would have meant that the triangle spun around.

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