7. Finding a Side
You have a tomato plant with a stake supporting it. They meet at a 14° angle, the stake meets the ground at a 77° angle, and the plant and stake are 6 inches apart. How tall is the tomato plant?
To use Law of Sines the formula is: Sin a/A = Sin b/B. The angles are 'a' and 'b' while the sides are represented by 'A' and 'B'
In this situation the formula is Sin14/6 = Sin77/B.
You crossmultiply after this giving you: 6Sin77=BSin14
Then divide both sides by Sin14 leaving you with: 24.2=B
In this situation the formula is Sin14/6 = Sin77/B.
You crossmultiply after this giving you: 6Sin77=BSin14
Then divide both sides by Sin14 leaving you with: 24.2=B
The tomato pal
8. Finding an Angle
You have a swing with a pointed roof, you let a vine grow over it. The length of the roof is 10 feet and the sides are 5 feet. One of the angles is 60°. What is the angle located at the top of the roof?
Using the same formula as the one before you use Sin a/A=Sin b/B.
Giving you Sin a/10=Sin60/5
You crossmultiply which leaves you with: 5sin a=10Sin60.
Now you can divide both sides by 5: 5Sin a/5=10Sin60/5
This leaves you with: 1.73=a
Giving you Sin a/10=Sin60/5
You crossmultiply which leaves you with: 5sin a=10Sin60.
Now you can divide both sides by 5: 5Sin a/5=10Sin60/5
This leaves you with: 1.73=a
So the angle is 1.73°.