Question

In triangle ABC, angle = 90 degrees. AC = 7, BC = 12. AB = _______ Measure of angle A = _______ Measure of angle B = _______

Answer 1

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

$tan \angle A = \frac{Opposite \, side \, to \, angle \, A}{Adjacent \, side \, to \, angle \, A} = \frac{BC}{AC} = \frac{12}{7} = 1.714$

∴ ∠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 2

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 °