Question

Identify all solutions for a triangle with A - 38°, b= 10, and a=8. Round to the nearest tenth.

Answer 1

B= 50.35°

C=91.65°

c= 12.77

Explanation:

Given:

A = 38°

b= 10 and a=8.

Required:

angles B and C, and sides c.

By using the rule for law of sines

`sin B=b(sinA)/(a) = ((10)(0.62))/(8)` => 0.77

B=
`sin^-^1`(0.77) => 50.35°

For angle C:

angle C= 180 - A - B => 180 - 38 - 50.35

=91.65°

For side c:

c=
`a((sinC)/(sinA) )` => 8(
`(0.99)/(0.62)`)

c= 12.77

Answer 2

A=38 degrees, B=50 degrees, C=92 degrees

a=8, b=10, c=13

Explanation:

Given a triangle where: A=38°, b= 10, and a=8.

Using Law of Sines

`(a)/(sin A) =(b)/(sin B) \\(8)/(sin 38) =(10)/(sin B) \\$Cross multiply\\8 X sin B=10 X Sin 38\\Sin B=(10 X sin 38)/ 8\\B=arcsin[(10 X sin 38)/ 8]\\B\approx50^\circ`

`\angle A+\angle B+\angle C=180^\circ($Sum of angles in a triangle)\\38+50+\angle C=180^\circ\\\angle C=180-88\\\angle C=92^\circ`

`(a)/(sin A) =(c)/(sin C) \\(8)/(sin 38) =(c)/(sin 92) \\$Cross multiply\\8 X sin 92=c X Sin 38\\c=(8 X sin 92)/ sin38\\c\approx13`