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asambeis [7]
1 year ago
12

Find the length of arc AD. Use 3.14for r. Round to the nearest tenth.7.9 cmB66.4DС[? ]cmEntar

Mathematics
1 answer:
ch4aika [34]1 year ago
5 0

The first thing we must do is calculate the circumeference:

\begin{gathered} c=2\cdot\pi\cdot r \\ c=2\cdot3.14\cdot7.9 \\ c=49.612 \end{gathered}

now, calculate the angle of arc

360° = 49.612

360° - 66.4° - 180° = x

x = 113.6°

now, to calculate the arc length it would be:

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<h3>Answers:</h3>

14.  Each leg is   21\sqrt{2}  units long.

15 (a). The longer leg is 7\sqrt{3}  units long

15 (b). The hypotenuse is 14 units long

=====================================================

Explanations:

For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say

y = x\sqrt{2} where x is the leg and y is the hypotenuse

Let's solve for x

y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}\\\\

Now plug in the given hypotenuse y = 42, this leads to,

x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}\\\\

---------------------------

For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.

The longer leg is equal to sqrt(3) times the short leg. The longer leg is 7\sqrt{3}

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