Alright, lets get started.
A right triangle (triangle 1) has a hypotenuse length of 115 mm and α = 31.2°. What are the measurements for a, b, and β?
Please refer the diagram I have attached.
Using SOH CAH TOA,
[tex]sin 31.2 = \frac{b}{115}[/tex]
[tex]b = 115 sin31.2[/tex]
Plugging the value of sin 31.2
[tex]b = 115*0.518 = 59.57[/tex] mm
Similarly,
[tex]cos31.2 = \frac{a}{115}[/tex]
[tex]a = 115cos31.2[/tex]
Plugging the value of cos 31.2
[tex]a = 115*.8553 = 98.36[/tex] mm
Now, for angle β
tan β = [tex]\frac{98.36}{59.57}[/tex]
tan β = 1.65
Using tan inverse
β = 58.78°
So, the answer is a = 98.36 mm, b = 59.57 mm and β = 58.78° : Answer
Hope it will help :)
A right triangle (triangle 1) has measurements of a = 505 mm and b = 286 mm. What are the measurements for c, α, and β?
Please refer the diagram I have attahced.
a and b are given, we could side c by using Pythagorean theorem.
[tex]c^2 = a^2 +b^2[/tex]
[tex]c^2 = 505^2 + 286^2[/tex]
[tex]c^2 = 255025+81796[/tex]
[tex]c^2 = 336821[/tex]
Taking square root on both sides
c = 580.36 mm
Using SOH CAH TOA,
tan α = [tex]\frac{505}{286}[/tex]
taking tan inverse
α = 60.48°
Similarly,
tan β = [tex]\frac{286}{505}[/tex]
taking tan inverse
β = 29.52°
So, the answer is c = 580.36 mm, α = 60.48° and β = 29.52° : Answer
Hope it will help :)
