Answer
Angle A = 47°
Angle B = 43°
Side AB = 51.7
Step-by-step explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is θ, the trignometric ratios in short forms are written as
SOH, CAH and TOA
SOH means Sin θ = (Opp/Hyp)
CAH means Cos θ = (Adj/Hyp)
TOA means Tan θ = (Opp/Adj)
So, the one to be used depends on the sides of the triangle that are provided.
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question, using Angle A as the non-right-angle angle,
Hypotenuse = AB = ?
Opposite = CB = a = 38
Adjacent = AC = b = 35
Angle = A = ?
We will solve for AB first
a² + b² = (hyp)²
CB² + AC² = AB²
38² + 35² = AB²
1444 + 1225 = AB²
2669 = AB²
AB² = 2669
Take the square root of both sides
√(AB²) = √(2669)
AB = 51.7
Then, we solve for Angle A
TOA means Tan A = (Opp/Adj)
Tan A = (38/35)
Tan A = 1.0857
A = Tan⁻¹ (1.0857)
A = 47°
For Angle B
Sum of angles in a triangle is 180°
A + B + C = 180°
47° + B + 90° = 180°
B + 137° = 180°
B = 180° - 137°
B = 43°
Hope this Helps!!!