Find the value of a.

Mathematics

2 answers:

Sergeeva-Olga [200]3 years ago

7 0

Answer:

mthway

Step-by-step explanation:

math*

shusha [124]3 years ago

3 0

= 81° + a° + a° = 180° ( angle sum property )

$81° + 3a = 180° \\ 3a = 180 - 81 \\ 3a = 99 \\ a = \frac{99}{3} \\ a = 33°$

The three angles of this triangle are :

$\: ∠1 \:= 81° \\ \: \: ∠2 = 2a = 2 \times 33 = 66° \\ ∠3 = a = 33 \\ \\ ∴ \: a = 33° \:$

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Answer:

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Step-by-step explanation:

To find the intersection points of the line and the circle we have to set up a system with their equations and solve. The system would look like this:

$\left \{ {{x=1 } \atop {x^2+y^2=16}} \right.$

To solve, substitute 1 for x in the second equation to get:

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Solving, we get:

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Therefore, the two points of intersection are $(1,\sqrt{15} )$ and $(1,-\sqrt{15})$ . The distance between these two points (the length of the chord in the circle) is $2\sqrt{15}$ which is 7.745966692414... which is 7.7 rounded to the nearest tenth.