Question:The sides of the triangle ABC are 3 cm, 3 cm and 5 cm. The sides of the triangle XYZ are 9 cm, 12 cm and 15 cm. If the area of the  triangle ABC is 6 `cm^2` , find the area of the triangle XYZ is 54 `cm^2` . 

Each side of the triangle XYZ is three times the corresponding side of the triangle ABC. The area of XYZ is therefore nine times as great as the area of ABC. Therefore the area of the triangle XYZ is 54 `cm^2` .

Question:A bottle holds 1 litre. How much would a similar bottle, in which each length is doubled, hold? 

The ratio of the linear lengths is 2:1.
   The ratio of the volumes is `2^3:1^3` or 8:1.
The second bottle therefore holds 8 litres.

Question:In the triangle ABC, the angle B=`90^0`, the angle A=`42^0` and AC=10 cm. Find the length of BC. 

Considering the angle A, the side BC is the opposite side and AC is the hypotenuse. Therefore sin `42^0`=`BC/10`
`:.` CB=10 sin `42^0` cm = `10 xx 0.6691 cm = 6.691 cm`
           = 6.69 cm (correct to 3 sig. fig.).

Question:In the triangle ABC, the angle B=`90^@` and the angle A=`38^@`, Given that BC=4 cm, calculate the Length of AB. 

The tangent of the angle A=`(BC)/(AB)` . The unknown side is the denominator of the fraction. Therefore consider the angle C.
The angle C = `90^@` - `38^@` = `52^@`
                                 `:. tan 52^@ = (AB)/4`
`:.` 4 tan `52^@` cm = `4 xx 1.2799 cm`
                                    = 5.1196 cm
                                    = 5.12 cm (correct to 3 sig. fig.).

Question:A ladder of length 5 m rests with its foot on horizontal ground and leans against a vertical wall. If the inclination of the ladder to the horizontal is `47^@` , find the distance of the foot of the ladder from the wall. 

If x meters, is the distance of the foot of the ladder from the wall.

cos `47^@` = `x/7`
`:.`    x = 5 cos `47^@`
          = `5 xx 0.6820`
          = 3.410
          = 3.41 (correct to 3 sig. fig.).
The foot of the ladder is 3.41 m from the wall.