Chapter 8.7, Problem 7WE

To determine

To find: the difference of shadow length of M and H.

Answer to Problem 7WE

The height of H is larger than M by 63 cm.

Explanation of Solution

Given:

The angle of elevation of sun for M is $70°$ .

Height of M is 180 cm.

The angle of elevation of sun for H is $35°$ .

Height of M is 90 cm.

Calculation:

M and H in sun are shown below:

  

Here, AB is the height of M and PQ is the height of H.

Take tan of angle $\angle ACB$ for the length of M as follows:

  $\begin{array}{c}\tan \angle ACB=\frac{AB}{BC}\\ \tan 70°=\frac{180}{BC}\\ BC=65.5\text{cm}\end{array}$

Take tan of angle $\angle PRQ$ for the length of H as follows:

  $\begin{array}{c}\tan \angle PRQ=\frac{PQ}{QR}\\ \tan 35°=\frac{90}{QR}\\ QR=128.5\text{cm}\end{array}$

Thus, the height of H is larger than M by 63 cm.