31. Five mark exercise problems VII

1. Find the area of a right triangle whose hypotenuse is $10 \ cm$ and one of the acute angle is $24^{\circ} 24'$.

 

Answer:

 

The area of a right triangle $=$  $cm^2$

 

2. In the given figure, $HT$ shows the height of a tree standing vertically. From a point $P$, the angle of elevation of the top of the tree (that is $\angle P$) measures $42^{\circ}$ and the distance to the tree is $60$ metres. Find the height of the tree.

 

 

Answer:

 

The height of the tree $=$  $m$

 

(Note: Round off the answers to $2$ decimal places.)