Answer:
a) Applying Pithagoras Theorem
b) Trigonometric relations
c) No we can not
d) No we can not
e) See step-by-step explanation
f) See step-by-step-explanation
Step-by-step explanation:
a) The easiest method for calculating the missing side is applying Pithagoras Theorem
c² = a² + b²
c² = (5)² + (12)² ⇒ c² = 25 + 144 ⇒ c² = 169 ⇒ c = 13
b) The easiest method to find the missing angles, is to calculate the sin∠ and then look for arcsin fuction in tables.
sin ∠α = 5/13 sin ∠α = 0.3846 ⇒ arcsin (0.3846 ) α = 23⁰
Now we can either get the other angle subtracting 180 - 90 - 23 = 67⁰
Or calculating sinβ = 12 /13 sinβ = 0.9230 arcsin(0.9230) β = 67⁰
c) The law of cosines should not be applied to right triangles, in fact for instance in our particular case we have:
Question a)
c² = a² + b² - 2*a*b*cos90⁰ (law of cosines ) but cos 90⁰ = 0
then c² = a² + b² which is the expression for theorem of Pithagoras
In case you look for calculating the missing angles
c² = a² + b² - 2*5*13*cos α
169 = 25 + 144 - 2*5*13* cos α
As you can see 169 - 25 - 144 = 0
Then we can not apply law of cosine in right triangles, we shoul apply trigonometric relations and Pithagoras theorem, and as we saw you can get the expression of Pithagoras theorem from cosine law
c² = a² + b² - 2*a*b*cos∠90° cos ∠ 90° = 0
Then c² = a² + b²
