<h2>Answer 1
</h2>
∠mB = 39°
BA= 14.30 inches.
CA= 11.1126 inches.
<u>Step by step explanation: </u>
Given one angle and one side:
∠A= 51°
∠mB= ?
As, it is a right angled triangle therefore, ∠C= 90
Also, sum of measure of triangle is 180:
∠mA + ∠mB + ∠mC = 180°
51° + ∠mB + 90° = 180°
∠mB = 180° - 90° - 51°
∠mB = 39° (Answer)
Now to calculate the required sides:
Given, BC= 9 inch (perpendicular)
BA= ? (hypotenuse) & CA= ? (base)
To find BA=
Since, perpendicular is given and we have to find hypotenuse. We will put the formula:
Sin ∠mB = Perp/ Hyp
Sin 39° = 9/ BA
BA= 9/ 0.629
BA= 14.30 inches.
For side CA, we will use Pythagorean Theorem:
Hyp2 = Perp2 + Base2
BA2 = BC2 + CA2
(14.30)2 = 92 + CA2
204.49 = 81 + CA2
CA2 = 123.49
Taking square root on both sides: weget,
CA= 11.1126 inches.
<h2>Answer 2
</h2>
∠mA = 37°
BC = 3.993 m.
CA = 3 m.
<u>Step by step explanation:</u>
Given one angle and one side:
∠mB = 53°
∠mA= ?
As, it is a right angled triangle therefore, ∠C= 90°
Also, sum of measure of triangle is 180:
∠mA + ∠mB + ∠mC = 180°
∠mA + 53° + 90° = 180°
∠mA = 180° - 143°
∠mA = 37°
Now to calculate the required sides:
Given, CB= ?(perpendicular)
BA= 5 m (hypotenuse) & CA= ? (base)
To find CB=
Since, hypotenuse is given and we have to find perpendicular. We will put the formula:
Sin ∠mA = Perp/ Hyp
Sin 37 = CB/ 5
0.601 = CB / 5
0.601 x 5 = CB
CB = 3.009 m.
For side CA, we will use Pythagorean Theorem:
Hyp2 = Perp2 + Base2
BA2 = CB2 + CA2
52 - 3.0092 = CA
15.94 = CA2
Taking square root on both sides: we get,
CA = 3.99 m.
<h2>Answer 3</h2>
m∠B = 62°
AB= 62.41 ml
CB= 55.10 ml.
<u>Step by step explanation</u>
Given one angle and one side,
∠mA= 28°
∠mB= ?
As, it is a right angled triangle therefore, ∠C= 90°
Also, sum of measure of triangle is 180:
∠mA + ∠mB + ∠mC = 180°
28° + m∠B + 90° = 180°
118° + m∠B = 180°
m∠B = 180° - 118°
m∠B = 62°
Now to calculate the required sides:
Given, CA= 29.3 ml (perpendicular)
AB= ? (hypotenuse) & CB= ? (base)
To findAB=
Since, perpendicular is given and we have to find hypotenuse. We will put the formula:
Sin ∠mA = Perp/ Hyp
Sin 28° = 29.3 / AB
0.469 = 29.3 / AB
AB = 29.3 / 0.469
AB= 62.41 ml
For side CA, we will use Pythagorean Theorem:
Hyp2 = Perp2 + Base2
AB2 = CA2 + CB2
62.41 = 29.3 + CB2
CB2 = 3036.59
Taking square root on both sides:
CB= 55.10 ml.
<h2>Answer 4</h2>
m∠B= 66°
AC= 5.694 m
CB = 12.78m.
<u>Step by step explanation:
</u>
Given one angle and one side,
∠mA= 24°
∠mB= ?
As, it is a right angled triangle therefore, ∠C= 90°
Also, sum of measure of triangle is 180:
∠mA + ∠mB + ∠mC = 180°
24° + m∠B + 90° = 180°
114° + m∠B = 180°
m∠B = 180° - 114°
m∠B= 66°
Now to calculate the required sides:
Given, AB=14 m (hypotenuse)
AC= ? (perpendicular) & CB= ? (base)
To find AC =
Since, hypotenuse is given and we have to find perpendicular. We will put the formula:
Sin ∠mA = Perp/ Hyp
Sin 24° = AC/ 14
0.406 = AC / 14
AC= 5.694 m
For side CB, we will use Pythagorean Theorem:
Hyp2 = Perp2 + Base2
AB2 = AC2 + CB2
14 = 5.694 + CB2
CB2 = 163.574
Taking square root on both side:
CB = 12.78m.
