Right triangle

Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?

Result

b =  7.746 ft
A =  61.045 °
B =  28.955 °

Solution:

c=16 ft a=14 ft  b=c2−a2=162−142≐2 15≐7.746≐7.746 ftc=16 \ \text{ft} \ \\ a=14 \ \text{ft} \ \\ \ \\ b=\sqrt{ c^2-a^2 }=\sqrt{ 16^2-14^2 } \doteq 2 \ \sqrt{ 15 } \doteq 7.746 \doteq 7.746 \ \text{ft}
sin⁡A=a:c A=180∘π⋅arcsin⁡(a/c)=180∘π⋅arcsin⁡(14/16)≐61.045≐61.045∘≐61∘2′42"\sin A=a:c \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(a/c)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(14/16) \doteq 61.045 \doteq 61.045 ^\circ \doteq 61^\circ 2'42"
B=90−A=90−61.045=5791200=28.955=28.955∘=28∘57′18"B=90 - A=90 - 61.045=\dfrac{ 5791 }{ 200 }=28.955=28.955 ^\circ =28^\circ 57'18"

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