Chapter 9.6, Problem 3PSA

a.

To determine

To calculate: The missing side where the other two sides are $240$ and $70$

Answer to Problem 3PSA

The required missing side is $250$

Explanation of Solution

Given: The other two sides are $240$ and $70$

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

  ${\left(x\right)}^2={\left(240\right)}^2+{\left(70\right)}^2$

  $x=\sqrt{57600+4900}$

  $x=\sqrt{62500}$

  $x=250$

Conclusion: Hence, the required missing side is $250$

b.

To determine

To calculate: The missing side where the other two sides are $50$ and $14$

Answer to Problem 3PSA

The required missing side is $48$

Explanation of Solution

Given: The other two sides are $50$ and $14$

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

  ${\left(50\right)}^2={\left(x\right)}^2+{\left(14\right)}^2$

  $x=\sqrt{2500-196}$

  $x=\sqrt{2304}$

  $x=48$

Conclusion: Hence, the required missing side is $48$

c.

To determine

To calculate: The missing side where the other two sides are $96$ and $100$

Answer to Problem 3PSA

The required missing side is $28$

Explanation of Solution

Given: The other two sides are $96$ and $100$

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

  ${\left(100\right)}^2={\left(96\right)}^2+{\left(x\right)}^2$

  $x=\sqrt{10000-9216}$

  $x=\sqrt{784}$

  $x=28$

Conclusion: Hence, the required missing side is $28$

d.

To determine

To calculate: Themissing side where the other two sides are $2.5$ and $0.7$

Answer to Problem 3PSA

The required missing side is $2.4$

Explanation of Solution

Given: The other two sides are $2.5$ and $0.7$

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

  ${\left(2.5\right)}^2={\left(x\right)}^2+{\left(0.7\right)}^2$

  $x=\sqrt{6.25+0.49}$

  $x=\sqrt{5.76}$

  $x=2.4$

Conclusion: Hence, the required missing side is $2.4$

e.

To determine

To calculate: The missing side where the other two sides are $275$ and $77$

Answer to Problem 3PSA

The required missing side is $264$

Explanation of Solution

Given: The other two sides are $275$ and $77$

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

  ${\left(275\right)}^2={\left(x\right)}^2+{\left(77\right)}^2$

  $x=\sqrt{75625-5929}$

  $x=\sqrt{69696}$

  $x=264$

Conclusion: Hence, the required missing side is $264$