Answer:
Step-by-step explanation:
Things we already know:
Angle B = 56 degrees
Angle C = 90 degrees
Side CB = 7 units
We need to find angle A and sides AC and AB.
We know that every triangle has its angles equal to 180 degrees
angle A + B + C = 180 degrees
angle A + 56 + 90 = 180 degrees
angle A + 146 = 180 degrees
subtract 146 from both sides.
angle A = 34 degrees
Now we know angle A.
To find side AC, we can use the tangent of theta.
The hyp (hypothenuse) = AB
The adjacent side = CB
And the opposite side = AC
The tangent of theta is the opposite side divided by the adjacent side.
[tex]tan(56) = \frac{AC}{7}[/tex]
Now we just need to solve for AC.
multiply 7 on both sides, to cancel it out on the right side.
7tan(56) = AC
10.3 = AC
Now we know the side AC.
AC = 10.3 units
To find the hypothenuse, we can use the sine, cosine, or the Pythagorean theorem.
I will choose the Pythagorean theorem, though.
[tex]7^{2} +10.3^{2} =AB[/tex]^2
49 +106.09 = AB^2
AB = 155.09 units^2
AB = 12.4 units
And now we know everything about this triangle.
A = 34 degrees
C = 90 degrees
B = 56 degrees
AC = 10.3 units
CB = 7 units
AB = 12.4 units
Hope I Helped!
