Question

In the following triangle, find the values of the angles B and B, which are the
best approximations to the solutions to this ambiguous case?
10
8.2
8.2
)45°
B
BY
A. B = 55° or B = 125°
B. B = 67° or B = 102.2°
C. B = 62.4° or B = 117.6°
D. B = 59.6° or B = 120.40

Answer 1

Answer: option D. B = 59.6° or B' = 120.4°

Step-by-step explanation:

Since the law is a/sinA = b/sinB = c/sinC you can try and verify each of them, by

10/sin(B)=......

and only B = 59.6° or B' = 120.4° give you the closed to 8.2/sin(45)= 11.59655121 which was 11.59401915.

(why the closed? because the question said it is "approximated")

Answer 2

The values of angles B and B' will be 59.6° and 120.4°, i.e. option C is the correct answer.

What is triangle ?

Triangle is a three sides two dimensional surface having three angles.

We have,

A triangle in which,

One of the angle is 45°, and the side opposite to angle 45° is 8.2 with corresponding angle B.

And the side opposite to angle B is 10.

Now,

Using the law of sine,

i.e.

$\frac{SinA}{a} =\frac{SinB}{b} =\frac{Sin c}{c}$

So,

According to the given triangle,

We get,

$\frac{Sin 45^0}{8.2} = \frac{Sin B}{10}$

We get,

$Sin B=\frac{Sin 45^0}{8.2} *10$

On solving we get,

⇒

$SinB= 59.58^0\ \ or\ \ SinB= 120.42$

i.e.

$SinB= 59.6^0 \ \ or\ \ SinB'= 120.40$

So,

The option C is the correct answer.

Hence, we can say that the values of angles B and B' will be 59.6° and 120.4°, i.e. option C is the correct answer.

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