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.)