Chapter 9, Problem 3RP

a

To determine

To find:The missing length in figure a

Answer to Problem 3RP

The missing length is $x=30$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $16$ and $34$

Formula used:Pythagoras theorem has been applied

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${16}^2+x^2={34}^2$

Thus, we get

  $x=30$

b

To determine

To find:The missing length in figure b

Answer to Problem 3RP

The missing lengths are $x=5$ and $y=8.66$

Explanation of Solution

Given information:The following two side has been given in the right triangle

  $10$

Formula used:Basic trigonometric definitions have been used

Calculation:We know that the two sides will be

  $10\sin {30}^0=x=5$

  $10\sin {60}^0=y=8.66$

Hence, we get

  $x=5$ and $y=8.66$

c

To determine

To find:The missing length in figure c

Answer to Problem 3RP

The missing length is $x=7$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $24$ and $25$

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${24}^2+x^2={25}^2$

Thus, we get

  $x=7$

d

To determine

To find:The missing length in figure d

Answer to Problem 3RP

The missing length is $x=15$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $12$ and $9$

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${12}^2+9^2=x^2$

Thus, we get

  $x=15$

e

To determine

To find:The missing length in figure e

Answer to Problem 3RP

The missing length is $x=4\sqrt{5}$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $3\sqrt{5}$ and $5\sqrt{5}$

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${(3\sqrt{5})}^2+x^2={(5\sqrt{5})}^2$

Thus, we get

  $x=4\sqrt{5}$

f

To determine

To find:The missing length in figure f

Answer to Problem 3RP

The missing length is $x=9$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $40$ and $41$

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${40}^2+x^2={41}^2$

Thus, we get

  $x=9$

g

To determine

To find:The missing length in figure g

Answer to Problem 3RP

The missing lengthsare $x=8.66$ and $y=17.32$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $15$

Formula used:Pythagoras theorem has been used

Calculation:We calculate the sides as

  $15\tan {30}^0=x=8.66$

  $\frac{15}{\sin {60}^0}=y=17.32$

h

To determine

To find:The missing length in figure h

Answer to Problem 3RP

The missing length is $x=12.5$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $3.5$ and $12$

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${3.5}^2+{12}^2=x^2$

Thus, we get

  $x=12.5$

i

To determine

To find:The missing length in figure i

Answer to Problem 3RP

The missing length is $x=26$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $10$ and $24$

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras in the given right triangle, and we get

  ${10}^2+{24}^2=x^2$

Thus, we get

  $x=26$

j

To determine

To find:The missing length in figure j

Answer to Problem 3RP

The missing length is $x=y=4\sqrt{2}$

Explanation of Solution

Given information:The following two sides are given in the right triangle

  $8$

Formula used:Pythagoras theorem has been used

Calculation:For a right isosceles triangle, we know that

  $x=y=\frac{8}{\sqrt{2}}=4\sqrt{2}$