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3 years ago

Solving right triangles

Mathematics

1 answer:

Anna35 [415]3 years ago

4 0

<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.

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