Chapter 9.8, Problem 29E

To determine

Tofind:The value of $x$

Answer to Problem 29E

  $x\approx 24$

Explanation of Solution

Given information:

Concept Used:

In a right-angled triangle ABC, sine for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of hypotenuse and cosine of acute angle $\angle A$ is the ratio of length of side adjacent to angle $\angle A$ to the length of hypotenuse.

Calculation:

Basis definition we can say-

  $\begin{array}{l}\cos {51}^{\circ }=\frac{Adjacent}{Hypotenuse}\\ \Rightarrow 0.6293=\frac{a}{12}\\ \Rightarrow a=\left(0.6293\right)12\\ \Rightarrow a=7.5518\end{array}$

  $\begin{array}{l}\sin {51}^{\circ }=\frac{opposite}{Hypotenuse}\\ \Rightarrow 0.7771=\frac{c}{12}\\ \Rightarrow c=\left(0.7771\right)12\\ \Rightarrow c=9.3258\end{array}$

  $\begin{array}{l}\tan {29}^{\circ }=\frac{opposite}{adjacent}\\ \Rightarrow 0.5543=\frac{c}{b}\\ \Rightarrow 0.5543=\frac{9.3258}{b}\\ \Rightarrow b=\frac{9.3258}{0.5543}\\ \Rightarrow b=16.8244\end{array}$

  $\begin{array}{l}x=a+b\\ \Rightarrow x=7.5518+16.8244\\ \Rightarrow x=24.3762\\ \Rightarrow x\approx 24\end{array}$