right triangle?

Question

using a right triangle

b=4 opposite
c=6 hypo

find a = adj.
alpha and beta

please help

Answer 1

in a right triangle, A squared plus B squared = C squared.

So, A^2 + 4^2 = 6^2
A^2 + 16 =36
-16 -16
A^2 =20
Take the square root of both sides and you'll get A, the adjacent arm of the triangle.

Answer 2

All right triangles can be solved using the pythagorean theorem which states a^2 +b^2 = c^2.

So in your equation a=? b=4 and c=6...so

a^2+(4)^2=(6)^2
a^2+16=36
subtract 16 on both sides
a^2=20
square root both sides and
a=square root of 20

Answer 3

sin alpha = 4/6 = 2/3
alpha = 42 deg

beta = 180 -90 -42 = 48 deg

c^2 = a^2 + b^2

36 = a^2 + 16
a^2 = 20

a = v20

Answer 4

6^2=a^2 + 4^2
36= a^2 +16
-16
20=a^2
take the square root
a=2 root 5

Answer 5

Pathagorean theroem

Opp^2+Adj^2=Hyp^2
4^2+a^2=6^2
a^2=6^2-4^2
a=square root(6^2-4^2)
a=4.5

Answer 6

a = sqrt(6^2-4^2) = sqrt(20) = 2sqrt(5)

angle B = arcsin(4/6) = 41.81 degrees
angle = 90-41.81 = 48.19 gegrees

Answer 7

a^2 = 6^2 - 4^2

a = rt(20)

Sin beta = 4/6, and

sin alpha = rt(20)/6