**Example 1 :**

A ramp for unloading a moving truck, has an angle of elevation of 30°. If the top of the ramp is 0.9 m above the ground level, then find the length of the ramp.

**Solution :**

The side which is opposite to 90 degree is known as hypotenuse side, the side which is opposite to θ is known as opposite side and the remaining side is known as adjacent side.

In the given problem,we have to find the length of hypotenuse side and we know the length of opposite side.

AC = Hypotenuse side

AB = Opposite side

BC = Adjacent side

sin θ = opposite side/hypotenuse side

sin 30° = AB/AC

1/2 = 0.9/AC

AC = 0.9 x 2

AC = 1.8 m

Therefore, the length of ramp is 1.8 m.

**Example 2 :**

A girl of height 150 cm stands in front of a lamp-post and casts a shadow of length 150 **√**3 cm on the ground. Find the angle of elevation of the top of the lamp-post.

**Solution :**

In the given problem,we have to find the angle inclined C.

AC = Hypotenuse side

AB = Opposite side = 150 cm

BC = Adjacent side = 150 **√**3 cm

tan θ = opposite side/Adjacent side

tan θ = AB/BC

tan θ = 150/150 **√**3

tan θ = 1/**√**3

θ = 30°

**Example 3 :**

Suppose two insects A and B can hear each other up to a range of 2 m. The insect A is on the ground 1 m away from a wall and sees her friend B on the wall, about to be eaten by a spider. If A sounds a warning to B and if the angle of elevation of B from A is 30°, will the spider have a meal or not ? ( Assume that B escapes if she hears A calling )

**Solution :**

In the given problem,we have to the length of AB.

AC = Hypotenuse side

BC = Opposite side = 1 m

AC = Adjacent side

sin θ = Opposite side/Hypotenuse side

sin θ = BC/AB

sin 30° = 1/AC

1/2 = 1/AC

AC = 2 m

So, the spider B escapes.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**