Chapter 9.6, Problem 4PSA

a.

To determine

To find: The missing side of the triangle where the other two sides are $45$ and $24$ .

Answer to Problem 4PSA

The missing side is $51$

Explanation of Solution

Given: The measures of the two sides are as follows

AC = $45$

BC = $24$

Concept used: The Pythagoras theorem will be used which is given as follows:

  ${\left(AB\right)}^2={\left(BC\right)}^2+{\left(AC\right)}^2$

Where

AB is the hypotenuse of the triangle ABC.

BC is the base of the triangle ABC.

AC is the perpendicular of the triangle.

Calculation:

Here, the formula is

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

Let the missing side be x

  ${\left(x\right)}^2={\left(45\right)}^2+{\left(24\right)}^2$

  $x=\sqrt{2025+576}$

  $x=\sqrt{2601}$

  $x=51$

Conclusion: Hence, the missing side is $51$

b.

To determine

To find: The missing side of the triangle where the other two sides are $3$ and $1.6$

Answer to Problem 4PSA

The missing side is $3.4$

Explanation of Solution

Given:

Two sides are $3$ and $1.6$

Concept used:

The Pythagoras theorem will be used which is given as follows:

  ${\left(AB\right)}^2={\left(BC\right)}^2+{\left(AC\right)}^2$

Where

AB is the hypotenuse of the triangle ABC.

BC is the base of the triangle ABC.

AC is the perpendicular of the triangle.

Calculation:

Here, the formula is

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

  $x^2={\left(3\right)}^2+{\left(1.6\right)}^2$

  $x^2=9+2.56$

  $x=\sqrt{11.56}$

  $x=3.4$

Conclusion: Hence, the missing side is $3.4$

c.

To determine

To find: The missing side of the triangle where the other two sides are $85$ and $40$

Answer to Problem 4PSA

The missing side is $75$

Explanation of Solution

Given:

Two sides are $85$ and $40$

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

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

  $x^2={\left(85\right)}^2-{\left(40\right)}^2$

  $x^2=7225-1600$

  $x=\sqrt{5625}$

  $x=75$

Conclusion: Hence, the missing side is $75$

d.

To determine

To find:The missing side of the triangle where the other two sides are $\frac{3}{2}$ and $\frac{17}{10}$

Answer to Problem 4PSA

The missing side is $\frac{4}{5}$

Explanation of Solution

Given:

Two sides are $\frac{3}{2}$ and $\frac{17}{10}$

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

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

  $x^2={\left(\frac{3}{2}\right)}^2-{\left(\frac{17}{10}\right)}^2$

  $x^2=\frac{289}{100}-\frac{9}{4}$

  $x=\sqrt{\frac{64}{100}}$

  $x=\frac{4}{5}$

Conclusion: Hence, the missing side is $\frac{4}{5}$

e.

To determine

To find:The missing side of the triangle where the other two sides are $150$ and $170$

Answer to Problem 4PSA

The missing side is $80$

Explanation of Solution

Given:

Two sides are $150$ and $170$

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

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

  $x^2={\left(170\right)}^2-{\left(150\right)}^2$

  $x^2=28900-22500$

  $x=\sqrt{6400}$

  $x=80$

Conclusion: Hence, the missing side is $80$