Angle C is an inscribed angle of circle P. Angle C measures (-3x - 6)° and arc AB measures (-4x)° . Find x

2 answers:

5 0

To find angle c, the fourmula is 1/2 of the intercepted arc. so, this would be (-3x-6)=(-4x)/2, then bring the 2 over, (-3x-6)2=-4x, multiply the 2, -6x-12=-4x, -2x=12, simplify, x=-6

check by plugging in.

valkas [14]4 years ago

4 0

Answer:

$x=-6$

Step-by-step explanation:

Given that angle C is an inscribed angle of circle P. Angle C measures (-3x - 6)° and arc AB measures (-4x)° .

We know that inscribed angle in a circle is 1/2 of the arc of tha angle.

ARc of AB =-4x

Inscribed angle = -3x-6

$2(-3x-6) =-4x\\x=-6$

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Two lighthouses are located 60 miles from one another on a north-south line. If a boat is spotted S 21o E from the northern ligh

jasenka [17]

Answer:

(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.

Step-by-step explanation:

The triangle attached represents the given problem.

First, let us determine the distance of the Boat from each of the lighthouse.

In Triangle ABC,

∠A+∠B+∠C=180 degrees

21+∠B+16=180

∠B=180-37=143 degrees.

Using Law of Sines

$\frac{a}{Sin A}=\frac{b}{Sin B}\\\frac{a}{Sin 21^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\a*sin143=60*sin21\\a=60*sin21\div sin143\\a=35.73 miles$

Similarly

$\frac{c}{Sin C}=\frac{b}{Sin B}\\\frac{c}{Sin 16^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\c*sin143=60*sin16\\c=60*sin16\div sin143\\c=27.48 miles$