Question

A skyscraper casts a shadow 200 feet long. If the angle of elevation of the sun is 49 , then the height of the skyscraper is _____.

Answer 1

height of skysraper is( 200×tan49) is the answer... so value is it230.07feet..if 49 is in degree

Answer 2

Answer:

The skyscraper’s height is found to be 230.0737 feet

To find:

Skyscraper’s height

Solution:

Given :  

Skyscraper forms a shadow which is of 200 ft long  

Here, the sun’s angle of elevation is given as 49°. The sun’s angle of elevation is equal to the skyscraper’s elevation angle. This is because, the skyscraper is so high that one standing at the place where skyscraper forms its shadow cannot see the sun. Skyscraper hides the sun so both angle is equal.  

Hence, the skyscraper’s height  

$\begin{array} { c } { \tan 49 ^ { \circ } = \frac { \text {opposite} } { \text {Adjacent} } } \\\\ { \tan 49 ^ { \circ } = \frac { h } { 200 \mathrm { ft } } } \\\\ { h = \tan 49 ^ { \circ } \times 200 \mathrm { ft } } \\\\ { h = 1.1504 \times 200 \mathrm { ft } } \\\\ { h = 230.0737 \mathrm { ft } } \end{array}$

Thus, the height of the given skyscraper is 230.0737 ft considering its elevation angle is same as it is to the sun.