Question

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? 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?

Answer 1

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,

$sin 31.2 = \frac{b}{115}$

$b = 115 sin31.2$

Plugging the value of sin 31.2

$b = 115*0.518 = 59.57$ mm

Similarly,

$cos31.2 = \frac{a}{115}$

$a = 115cos31.2$

Plugging the value of cos 31.2

$a = 115*.8553 = 98.36$ mm

Now, for angle β

tan β = $\frac{98.36}{59.57}$

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.

$c^2 = a^2 +b^2$

$c^2 = 505^2 + 286^2$

$c^2 = 255025+81796$

$c^2 = 336821$

Taking square root on both sides

c = 580.36 mm

Using SOH CAH TOA,

tan α = $\frac{505}{286}$

taking tan inverse

α = 60.48°

Similarly,

tan β = $\frac{286}{505}$

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 :)