Chapter 9.6, Problem 15PSB

a.

To determine

To calculate: Themissing side of the triangle whose other sides are 42 and 150.

Answer to Problem 15PSB

The missing side is $144$

Explanation of Solution

Given:

Two sides are $42$ and $150$

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 missing side be x

  ${\left(150\right)}^2={\left(42\right)}^2+x^2$

  $22500-1764=x^2$

  $20736=x^2$

  $x=144$

Conclusion: Hence, the missing side is $144$

b.

To determine

To calculate:Themissing side of the triangle whose other sides are $\frac{5}{8}$ and $\frac{1}{2}$ .

Answer to Problem 15PSB

The missing side is $\frac{3}{8}$

Explanation of Solution

Given:

Two sides are $\frac{5}{8}$ and $\frac{1}{2}$

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

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  $\frac{25}{64}-\frac{1}{4}=x^2$

  $\frac{25-16}{64}=x^2$

  $x=\frac{3}{8}$

Conclusion: Hence, the missing side is $\frac{3}{8}$

c.

To determine

To calculate:Themissing side of the triangle whose other sides are $\sqrt{4}$ and $\sqrt{3}$ .

Answer to Problem 15PSB

The missing side is $\sqrt{7}$

Explanation of Solution

Given:

Two sides are $\sqrt{4}$ and $\sqrt{3}$

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

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  $x^2={\left(\sqrt{4}\right)}^2+{\left(\sqrt{3}\right)}^2$

  $x^2=4+3$

  $x=\sqrt{7}$

Conclusion: Hence, the missing side is $\sqrt{7}$