Question

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

see the attached figure to better understand the problem  

Step 1

Find the value of c

we know that

Applying the Pythagorean Theorem

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

we have

$a=505\ mm$

$b=286\ mm$

substitute the values in the formula

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

$c^{2} =336,821$

$c=580.36\ mm$  

Step 2

Find the value of angle A (α)

we know that

in the right triangle ABC

$cos(A)=\frac{b}{c} \\ \\cos(A)=(286/580.36)\\ \\A=arc\ cos(286/580.36)\\ \\A=60.48\ degrees$

Step 3

Find the angle B (β)

we know that

in the right triangle ABC

angle A and angle B are complementary angles

so

A+B=90

solve for B

B=90-A-------> B=90-60.48-----> B=29.52°

therefore

the answers are

a) the measure of side c is 580.36 mm

b) the measure of the angle α is 60.48°

c) the measure of the angle β is 29.52°