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 r

Question

6 days ago

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ight triangle (triangle 1) has measurements of a = 505 mm and b = 286 mm. What are the measurements for c, α, and β?

1 answer:

babunello [8.4K] · Answer 1 · 2026-03-21T14:59:28+03:00

Alright, let's begin.

A right triangle (Triangle 1) has a hypotenuse measuring 115 mm, and angle α = 31.2°. What are the dimensions for a, b, and angle β?

Please see the diagram I have provided.

Utilizing SOH CAH TOA,

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

$b = 115 sin31.2$

Substituting the value of sin 31.2

$b = 115*0.518 = 59.57$ mm

Likewise,

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

$a = 115cos31.2$

Substituting the value of cos 31.2

$a = 115*.8553 = 98.36$ mm

For angle β

tan β = $\frac{98.36}{59.57}$

tan β = 1.65

Using the tangent inverse

β = 58.78°

Thus, we have a = 98.36 mm, b = 59.57 mm, and β = 58.78°: Final Answer

I hope this is helpful:)

A right triangle (Triangle 1) has lengths of a = 505 mm and b = 286 mm. What are the dimensions for c, α, and β?

Refer to the diagram I’ve attached.

With sides a and b provided, we can find side c using the Pythagorean theorem.

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

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

$c^2 = 255025+81796$

$c^2 = 336821$ Taking the square root of both sides

c = 580.36 mm

Applying SOH CAH TOA,

tan α =

Taking the tangent inverse $\frac{505}{286}$

α = 60.48°

Similarly,

tan β =

Taking the tangent inverse $\frac{286}{505}$

β = 29.52°

Thus, the answer is c = 580.36 mm, α = 60.48° and β = 29.52°: Final Answer

I hope this is helpful:)