Aright triangle (triangle 1) has a hypotenuse length of 115 mm and α = 31.2°. what are the measurements for a, b, and β? 2. a right triangle (triangle 1) has measurements of a = 505 mm and b = 286 mm. what are the measurements for c, α, and β?

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,

Plugging the value of sin 31.2

mm

Similarly,

Plugging the value of cos 31.2

mm

Now, for angle β

tan β =

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.

Taking square root on both sides

c = 580.36 mm

Using SOH CAH TOA,

tan α =

taking tan inverse

α = 60.48°

Similarly,

tan β =

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 :)