**Trigonometry Practical Problems Using Angle of Elevation :**

Here we are going to see, some example problems based on angle of elevation.

In order to solve word problems, first draw the picture to represent the given situation.

To find the questions 1 and 2, please visit the page "Angle of Elevation Practice Problems".

To find the questions 3 and 5, please visit the page "Questions Based on Angle of Elevation".

**Question 6 :**

The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?

**Solution :**

Let DC = x, ED = 15 - x

Height of the electric pole = AB = DC

AD = BC

In triangle AED,

tan θ = Opposite side / Adjacent side

tan 30 = ED/AD

1/√3 = (15 - x)/AD

AD = (15 - x)√3 ----(1)

In triangle BCE,

tan 60 = EC/BC

√3 = 15/BC

BC = 15/√3

BC = (15/√3) ⋅ (√3/√3)

BC = 15√3/3 = 5√3----(2)

(1) = (2)

(15 - x)√3 = 5√3

15√3 - x√3 = 5√3

15√3 - 5√3 = x√3

x = 10√3/√3

x = 10

Hence the height of the electric pole is 10 m.

**Question 7 :**

A vertical pole fixed to the ground is divided in the ratio 1:9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 25 m away from the base of the pole, what is the height of the pole?

**Solution : **

By using angle bisector theorem,

Let the the two parts subtend equal angles at point A such that

CAB = DAC = θ

BC/DC = AB/AD

1/9 = 25/AD

AD = 25(9)

AD^{2} = AB^{2} + BC^{2}

225^{2} = 25^{2} + (10x)^{2}

100x^{2} = 225^{2} - 25^{2}

100x^{2 }= (225 + 25) (225 - 25)

100x^{2 }= (250) (200)

x^{2} = 500

x = 100√5 m

**Question 8 :**

A traveler approaches a mountain on highway. He measures the angle of elevation to the peak at each milestone. At two consecutive milestones the angles measured are 4° and 8° . What is the height of the peak if the distance between consecutive milestones is 1 mile. (tan 4° = 0.0699, tan 8° = 0.1405)

**Solution :**

Let BC = x

In triangle BDC,

tan 8 = DC/BC

0.1405 = DC/x

DC = 0.1405 x ----(1)

In triangle ADC,

tan 4 = DC/AC

0.0699 = DC/(1 + x)

DC = 0.0699(1 + x) ----(2)

(1) = (2)

0.1405 x = 0.0699(1 + x)

0.1405 x = 0.0699 + 0.0699 x

(0.1405 - 0.0699)x = 0.0699

0.0706 x = 0.0699

x = 0.0699/0.0706

x = 699/706

x = 0.99

By applying the value of x in (1), we get

DC = 0.1405 (0.99)

DC = 0.14 mile

Hence the height of peak is 0.14 mile.

After having gone through the stuff given above, we hope that the students would have understood, "Trigonometry Practical Problems Using Angle of Elevation".

Apart from the stuff given in this section "Trigonometry Practical Problems Using Angle of Elevation" if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**

**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**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**