Chapter 9.10, Problem 4PSA

a

To determine

To find:The value of x to the nearest integer

Answer to Problem 4PSA

The value of $x=18$

Explanation of Solution

Given information:The following information can be found from the table of trigonometric ratios

  $\sin {27}^0=0.4540$

Formula used:Basic sine identity has been used

Calculation:Now, we know that in the given figure, the value of

  $\sin {27}^0=\frac{x}{40}=0.4540$

Hence, solving it for x , we get

  $x=18.16$

Hence, rounding off to the nearest integer, we get

  $x=18$

b

To determine

To find:The value of x to the nearest integer using the trigonometric tables given in the book.

Answer to Problem 4PSA

The value of $x=44$

Explanation of Solution

Given information:The following information can be found from the table of trigonometric ratios

  $\tan {32}^0=0.6249$

Formula used:Basic tangent identity has been used

Calculation:Now, we know that in the given figure, the value of

  $\tan {32}^0=\frac{x}{70}=0.6249$

Hence, solving it for x , we get

  $x=43.74$

Hence, rounding off to the nearest integer, we get

  $x=44$

c

To determine

To find:The value of xwhen one diagonal and angle is given of the rectangle.

Answer to Problem 4PSA

The value of $x=616$

Explanation of Solution

Given information:The following information can be found from the table of trigonometric ratios

  $\cos {52}^0=0.6157$

Formula used:Basic cosine identity has been used

Calculation:Now, we know that in the given figure, the value of

  $\cos {52}^0=\frac{x}{100}=0.6157$

Hence, solving it for x , we get

  $x=615.7$

Hence, rounding off to the nearest integer, we get

  $x=616$

d

To determine

To find:The value of xwhen side and angle of the rhombus is given.

Answer to Problem 4PSA

The value of $x=16$

Explanation of Solution

Given information:The following information can be found from the table of trigonometric ratios

  $\sin {23}^0=0.3907$

Formula used:Basic sine identity has been used

Calculation:Now, we know that in the given figure, the value of

  $\sin {23}^0=\frac{x}{40}=0.3907$

Hence, solving it for x , we get

  $x=15.63$

Hence, rounding off to the nearest integer, we get

  $x=16$