Respuesta :
Answer:
AB = 13.89
Measure of angle A = 59.74°
Measure of angle B = 30.26°
Step-by-step explanation:
The given parameters are;
∠C = 90°
AC = 7
BC = 12
Part 1
Hence, the question has the dimensions of the two adjacent sides of the right angle (angle 90°)
From Pythagoras theorem, we have;
A² = B² + C²
Where, A is the opposite side to the right angle, hence;
In the ΔABC,
AB ≡ A
Therefore;
AB² = AC² + BC² = 7² + 12² = 193
∴ AB = √193 = 13.89
Part 2
∠A is the side opposite side BC such that by trigonometric ratios
[tex]tan \angle A = \frac{Opposite \, side \, to \, angle \, A}{Adjacent \, side \, to \, angle \, A} = \frac{BC}{AC} = \frac{12}{7} = 1.714[/tex]
∴ ∠A = Arctan(1.714) or tan⁻¹(1.714) = 59.74°
Part 3
∠B is found from knowing that the sum of the angles in a triangle = 180°
∴ ∠A + ∠B + ∠C = 180° which gives
59.74° + 90° + ∠B = 180°
Hence, ∠B = 180° - (59.74° + 90°) = 180° - 149.74° = 30.26°.
Answer:
AB ≈ 13.89
Angle A = 59.74°
Angle B = = 30.26 °
Step-by-step explanation:
The diagram illustrated is a right angle triangle . Base on the question we are asked to find angle A and B. That means the angle been referred to as 90° is the angle C.
Using Pythagoras theorem the side AB can be solved below .The side AB is the hypotenuse of the triangle.
c² = a² + b²(Pythagoras theorem)
c² = 12² + 7²
c² = 144 + 49
c² = 193
square root both sides
c = √193
c = 13.8924439894
c ≈ 13.89
Angle A
Using tangential ratio
tan A = opposite/adjacent
tan A = 12/7
A = tan ⁻¹ 12/7
A = tan⁻¹ 1.71428571429
A = 59.7435628365
A = 59.74°
Angle B
The total angle in a triangle is 180° . Therefore the remaining angle B can be gotten when you subtract 90° plus 59.74° from 180°.
angle B = 180 - 90 - 59.74 = 30.26 °
