What is the value of N ?

Mathematics

2 answers:

Nady [450]3 years ago

7 0

Remember that a straight line = 180°

Angle next to 121°: 180 - 121 = 59
Angle next to 121° = 59°

Angle next to 144°: 180 - 144 = 36
Angle next to 144° = 36°

180 - 59 - 36 = 85

angle next to n = 85°

180 - 85 = 95

n = 95°, or D

hope this helps

Burka [1]3 years ago

3 0

The top angle in the middle triangle is 180-121, which is 59.
The right side angle in the triangle is 180-144, which is 36.

The angles of a triangle add up to 180. Therefore, bottom left angle in triangle equals 180-59-36, which equals 85.

N equals 180-the bottom left triangle angle, therefore it is 95 degrees.

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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

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