**Problems on Triangle in Trigonometry for Class 11 :**

Here we are going to see some example problems on triangle in trigonometry for class 11.

**Question 1 :**

In any triangle ABC, prove that the area triangle = b^{2} + c^{2} − a^{2}/4 cotA.

**Solution :**

Cosine formula :

cos A = (b^{2} + c^{2} - a^{2}) / 2bc

Given that :

= b^{2} + c^{2} − a^{2}/4 (cos A/sin A)

= (b^{2} + c^{2} − a^{2}) sin A/4 cos A ---(1)

From cosine formula, we have

2bc cos A = b^{2} + c^{2} - a^{2}

By applying the value of b^{2} + c^{2} - a^{2 }in (1)

= (2bc cos A) sin A/4 cos A

= (bc sin A)/2

= (1/2) bc sin A

= Area of triangle

Hence proved.

**Question 2 :**

In a triangle ABC, if a = 12 cm, b = 8 cm and C = 30°, then show that its area is 24 sq.cm.

**Solution :**

Area of triangle = (1/2) ab sin C

= (1/2) 12(8) sin 30°

= 48 (1/2)

= 24 square units.

Hence it is proved.

**Question 3 :**

In a triangle ABC, if a = 18 cm, b = 24 cm and c = 30 cm, then show that its area is 216 sq.cm.

**Solution :**

Since the length of all sides are different, we have to use heron's formula to find the area.

a = 18 cm, b = 24 cm and c = 30 cm

s = (a + b + c)/2

= (18 + 24 + 30)/2

= 72/2

s = 36

s - a = 36-18 = 18

s - b = 36-24 = 12

s - c = 36-30 = 6

Area of triangle = √s(s-a)(s-b)(s-c)

= √36(18)(12)(6)

= 216 square units.

Hence it is proved.

**Question 4 :**

Two soldiers A and B in two different underground bunkers on a straight road, spot an intruder at the top of a hill. The angle of elevation of the intruder from A and B to the ground level in the eastern direction are 30° and 45° respectively. If A and B stand 5km apart, find the distance of the intruder from B.

**Solution :**

<A = 30

<B + 45 = 180

<B = 180 - 45 = 135

<A + <B + <C = 180

30 + 135 + <C = 180

<C = 180 - 165

<C = 15

BC = a, AC = b and AB = c

Sine formula :

a/sin A = b/sin B = c/sin C

a/sin 30 = b/sin 135 = 5/sin 15

a/(1/2) = 5/sin (45-30)

2a = 5/sin (45-30)

sin (45-30) = sin 45 cos 30 - cos 45 sin 30

= (1/√2)(√3/2) - (1/√2)(1/2)

= √3/2√2 - 1/2√2

= (√3 - 1)/2√2

2a = 5/[(√3 - 1)/2√2]

2a = 10√2/(√3 - 1)

a = 5√2/(√3 - 1)

After having gone through the stuff given above, we hope that the students would have understood, "Problems on Triangle in Trigonometry for Class 11"

Apart from the stuff given in "Problems on Triangle in Trigonometry for Class 11", if you need any other stuff in math, please use our google custom search here.

Widget 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**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work 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**