Chapter 9.6, Problem 1PSA

a.

To determine

To calculate: Themissing side where the other two sides are $20$ and $15$

Answer to Problem 1PSA

The required missing side is $25$

Explanation of Solution

Given: The other two sides are $20$ 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

  ${\left(x\right)}^2={\left(20\right)}^2+{\left(15\right)}^2$

  $x=\sqrt{400+225}$

  $x=\sqrt{625}$

  $x=25$

Conclusion: Hence, the required missing side is $25$

b.

To determine

To calculate: Themissing side where the other two sides are $45$ and $27$

Answer to Problem 1PSA

The required missing side is $36$

Explanation of Solution

Given:

The other two sides are $45$ and $27$

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

  ${\left(45\right)}^2={\left(x\right)}^2+{\left(27\right)}^2$

  $x=\sqrt{2025-729}$

  $x=\sqrt{1296}$

  $x=36$

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

c.

To determine

To calculate: Themissing side where the other two sides are $28$ and $35$

Answer to Problem 1PSA

The required missing side is $21$

Explanation of Solution

Given:

The other two sides are $28$ and $35$

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

  ${\left(35\right)}^2={\left(28\right)}^2+{\left(x\right)}^2$

  $x=\sqrt{1225-784}$

  $x=\sqrt{441}$

  $x=21$

Conclusion: Hence, the required missing side is $21$

d.

To determine

To calculate: Themissing side where the other two sides are $1.34$ and $1$

Answer to Problem 1PSA

The required missing side is $1.672$

Explanation of Solution

Given:

The other two sides are $1.34$ and $1$

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

  ${\left(x\right)}^2={\left(1.34\right)}^2+{\left(1\right)}^2$

  $x=\sqrt{1.7956+1}$

  $x=\sqrt{2.7956}$

  $x=1.672$

Conclusion: Hence, the required missing side is $1.672$

e.

To determine

To calculate: Themissing side where the other two sides are $75$ and $45$

Answer to Problem 1PSA

The required missing side is $60$

Explanation of Solution

Given:

The other two sides are $75$ and $45$

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

  ${\left(75\right)}^2={\left(x\right)}^2+{\left(45\right)}^2$

  $x=\sqrt{5625-2025}$

  $x=\sqrt{3600}$

  $x=60$

Conclusion: Hence, the required missing side is $60$