Question

To find the measure of ∠A in ∆ABC, use the___(Pythagorean Theorem, Law of Sines, Law of Cosines). To find the length of side HI in ∆HIG, use the____(Pythagorean Theorem, Law of Sines, Law of Cosines) .

Answer 1

Answer: HOPE THIS HELPS

Answer 2

Part 1) To find the measure of ∠A in ∆ABC, use

we know that

In the triangle ABC

Applying the law of sines

`(a)/(sin\ A)=(b)/(sin\ B)=(c)/(sin\ C)`

in this problem we have

`(a)/(sin\ A)=(b)/(sin\ theta)\\ \\a*sin\ theta=b*sin\ A\\ \\ sin\ A=(a*sin\ theta)/(b) \\ \\ A=arc\ sin ((a*sin\ theta)/(b))`

therefore

the answer Part 1) is

Law of Sines

Part 2) To find the length of side HI in ∆HIG, use

we know that

In the triangle HIG

Applying the law of cosines

`g^(2)=h^(2)+i^(2)-2*h*i*cos\ G`

In this problem we have

g=HI

G=angle Beta

substitute

`HI^(2)=h^(2)+i^(2)-2*h*i*cos\ Beta`

`HI=\sqrt{h^(2)+i^(2)-2*h*i*cos\ Beta}`

therefore

the answer Part 2) is

Law of Cosines