4. SOH
A tree split in half from being struck by lightning. However they split in uneven lengths. If one side fell 10 feet up from the base and theta is 30° how long was the half?
The sides you're working with are the opposite and the hypotenuse. Therefore you use SOH or Sin. You're also given the angle of theta which 30°. This is insterted into the formula, which is Sinθ=10/h.
For this question it is Sin30=10/h.
You then cross multiply leaving you with: 10=hSin30.
You can then divide both sides by Sin30: 10/sin30=hSin30/Sin30
This leaves you with 20=h
For this question it is Sin30=10/h.
You then cross multiply leaving you with: 10=hSin30.
You can then divide both sides by Sin30: 10/sin30=hSin30/Sin30
This leaves you with 20=h
So the hypotenuse is 20 feet.
5. CAH
Say that you have a pot with a parasitic vine 5 feet from a particularly susceptible plant. Theta is 15°.How far would the vine have to reach to get to the susceptible plant?
You have the hypotenuse and adjacent so you use CAH,Cos.
Adjacent is 5 ft and you're looking for hypotenuse. The formula for this is Cosθ=adjacent/hypotenuse
In this case it is Cos15=5/a
You then move on to cross multiplying leaving you with: 5=aCos15.
You divide Cos15 from both sides: 5/Cos15=aCos15/Cos15
This leaves you with 5.2 ft=a
Adjacent is 5 ft and you're looking for hypotenuse. The formula for this is Cosθ=adjacent/hypotenuse
In this case it is Cos15=5/a
You then move on to cross multiplying leaving you with: 5=aCos15.
You divide Cos15 from both sides: 5/Cos15=aCos15/Cos15
This leaves you with 5.2 ft=a
So the vine would have to reach 5.2 feet.
6. TOA
You have a bonsai tree. The watering can is laying 52 inches away. The angle of descent is 32°. How tall is the tree.
You're using TOA since you're given the adjacent and opposite. The formula is Tan(θ)=opposite/adjacent
For this question the formula is Tan(32)=x/52
You cross multiply leaving you with: 52Tan(32)=x
Leaving you with 32.5 inches
For this question the formula is Tan(32)=x/52
You cross multiply leaving you with: 52Tan(32)=x
Leaving you with 32.5 inches
The tree is 32.5 inches