Chapter 9.6, Problem 2PSA

a.

To determine

To calculate: Themissing side where the other two sides are $24$ and $26$

Answer to Problem 2PSA

The required missing side is $10$

Explanation of Solution

Given:

The other two sides are $24$ and $26$

Concept used:

Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Let the other side be x

  ${\left(26\right)}^2={\left(24\right)}^2+x^2$

  $x=\sqrt{676-576}$

  $x=\sqrt{100}$

  $x=10$

Conclusion: Hence, the required missing side is $10$

b.

To determine

To calculate: Themissing side where the other two sides are $72$ and $30$

Answer to Problem 2PSA

The required missing side is $78$

Explanation of Solution

Given:

The other two sides are $72$ and $30$

Concept used:

Here, we are using Pythagoras theorem.

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Let the other side be x

  ${\left(x\right)}^2={\left(72\right)}^2+{\left(30\right)}^2$

  $x=\sqrt{5184+900}$

  $x=\sqrt{6084}$

  $x=78$

Conclusion: Hence, the required missing side is $78$

c.

To determine

To calculate: Themissing side where the other two sides are $39$ and $15$

Answer to Problem 2PSA

The required missing side is $36$

Explanation of Solution

Given:

The other two sides are $39$ and $15$

Concept used:

Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Calculation:

Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Let the other side be x

  ${\left(39\right)}^2={\left(x\right)}^2+{\left(15\right)}^2$

  $x=\sqrt{1521-225}$

  $x=\sqrt{1296}$

  $x=36$

Conclusion: Hence, the required missing side is $36$

d.

To determine

To calculate: Themissing side where the other two sides are $60$ and $25$

Answer to Problem 2PSA

The required missing side is $65$

Explanation of Solution

Given:

The other two sides are $60$ and $25$

Concept used:

Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Calculation:

Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Let the other side be x

  ${\left(x\right)}^2={\left(60\right)}^2+{\left(25\right)}^2$

  $x=\sqrt{3600+625}$

  $x=\sqrt{4225}$

  $x=65$

Conclusion: Hence, the required missing side is $65$

e.

To determine

To calculate: The missing side where the other two sides are $6$ and $2.5$

Answer to Problem 2PSA

The required missing side is $6.5$

Explanation of Solution

Given:

The other two sides are $6$ and $2.5$

Concept used:

Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Let the other side be x

  ${\left(x\right)}^2={\left(6\right)}^2+{\left(2.5\right)}^2$

  $x=\sqrt{36+6.25}$

  $x=\sqrt{42.25}$

  $x=6.5$

Conclusion: Hence, the required missing side is $6.5$