Question

Help fast please im so lost

Answer 1

Using the law of sines and the law of cosines, the solutions for the triangle are given as follows:

• A = 34.52º.

• B = 31.48º.

• c = 108.

What is the law of cosines?

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

• C is the angle opposite to side c.

• a and b are the lengths of the other sides.

For this problem, side c is found using the law of cosines, as follows:

c² = 67² + 62² - 2(67)(62)cos(114º)

c² = 11712.17

c = sqrt(11712.17)

c = 108.

What is the law of sines?

Suppose we have a triangle in which:

• The length of the side opposite to angle A is a.

• The length of the side opposite to angle B is b.

• The length of the side opposite to angle C is c.

The lengths and the sine of the angles are related as follows:

$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}$

Angle A can be found as follows:

$\frac{\sin{A}}{67} = \frac{\sin{114^\circ}}{108}$

$\sin{A} = \frac{67\sin{114^\circ}}{108}$

sin(A) = 0.5667365339

A = arcsin(0.5667365339)

A = 34.52º.

The sum of the internal angles of a triangle is of 180º, hence we use it to find angle B as follows:

34.52 + B + 114 = 180

B = 180 - (34.52 + 114)

B = 31.48º.

More can be learned about the law of sines at brainly.com/question/25535771

#SPJ1