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sukhopar [10]
3 years ago
11

State the size of angle OAB, giving a reason for your answer

Mathematics
1 answer:
lina2011 [118]3 years ago
5 0

Answer:

OAB is 90°

Explanation -

Given - A circle with centre O

According to the theorem , The tangent of a circle and the line of tangency make an angle of 90°

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In a triangle, two sides that measure 8 centimeters and 11 centimeters form an angle that measures 82°. to the nearest tenth of
Gwar [14]
We can use the Сosine formula to solve this problem.
<span>First we must find the third side (АС) of the triangle:
</span>
AC^2=AB^2+BC^2-2*AB*BC*cos82^o \\ AC^2=8^2+11^2-2*8*11*0.1392 \\ AC^2=64+121-24.4992= 160.508 \\ AC= \sqrt{160.508} \approx  12.67 \ cm
<span>
The smallest angle of the triangle lies opposite the smallest side, so we need to find m</span>∠C.

cosC= \frac{AC^2+BC^2-AB^2}{2*AC*BC}  \\  \\ cosC= \frac{12.67^2+11^2-8^2}{2*12.67*11}= \frac{160.53+121-64}{278.74} = \frac{217.53}{278.74} \approx  0.7804

Now we can use Bradis's Table (I don't know the name in English, maybe Trigonometric Table?) to find m∠C:

m∠С = 38°42' = 38.7°

Answer: 38.7°


<span>I hope this helps</span>

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3 years ago
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tino4ka555 [31]
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