Question

Angelique draws triangle ghk. if angle g=30o, g=3, ang k=4, what is the approximate length of h

A. 1.2 or 5.7
B. 2.2 or 4.7
C. 4.7
D. 5.7

Answer 1

A) 1.2 or 5.7

Explanation:

got it right on edge :)

Answer 2

To solve this problem we will use the cosine rule. Formula is:

`x^(2) = y^(2) + z^(2) -2*y*z*cos \alpha`
On left side we have side that we want to find length of. On right side we have other two sides and angle opposite to searched side.

We are given:
angle g=30°
g = 3
k = 4

In case of our formula we know x and y, but we do not know z. Now we have:

`3^(2) = 4^(2) + z^(2) -2*4*z*cos 30`

`9 = 16 + z^(2) -2*4*z* ( √(3) )/(2) \\ 9=16+z^(2) -4√(3) z \\ z^(2)-4√(3) z+7=0`

Now we solve this for z:

`c_(1) = \frac{-b+ \sqrt{ b^(2)-4ac} }{2a} \\ c_(1) = (4 √(3)+ √(48-28) )/(2) \\ c_(1) = (4 √(3)+ √(20) )/(2) \\ c_(1) = (4 √(3)+ 2√(5) )/(2) \\ c_(1) =2 √(3) + √(5) =5.7`


`c_(2) = \frac{-b- \sqrt{ b^(2)-4ac} }{2a} \\ c_(2) = (4 √(3)- √(48-28) )/(2) \\ c_(2) = (4 √(3)- √(20) )/(2) \\ c_(2) = (4 √(3)- 2√(5) )/(2) \\ c_(2) =2 √(3) - √(5) =1.2`

Our solution is A.