Trigonometric ratios worksheet is much useful to the kids who would like to practice problems on right triangle in trigonometry.

1) In the right triangle PQR given below, find the six trigonometric ratios of the angle θ

2) In the right triangle PQR given below, find the six trigonometric ratios of the angle θ

3) In triangle ABC, right angled at B, 15 sin A = 12. Find the other five trigonometric ratios of the angle A. Also find the six ratios of the angle C

4) In the right triangle PQR given in question no.2, find the value of sinθ and cosθ. Using them, find the value of tanθ and cotθ

5) In the right triangle ABC given in question no.3, find the value of sinθ and cosθ. Using them, find the value of tanθ and cotθ

**Problem 1 :**

From the figure given below, find the six trigonometric ratios of the angle θ.

**Solution :**

From the figure given above,

opposite side = 5

adjacent side = 12

hypotenuse = 13

Therefore,

**Problem 2 :**

From the figure given below, find the six trigonometric ratios of the angle θ.

**Solution : **

From the figure given above, AC = 24 and BC = 7.

By Pythagorean theorem,

AB² = BC² + CA²

AB² = 7² + 24²

AB² = 49 + 576

AB² = 625

AB² = 25²

AB = 25

Now, we can use the three sides to find the six trigonometric ratios of angle θ.

Therefore,

**Problem 3 :**

In triangle ABC, right angled at B, 15 sin A = 12. Find the other five trigonometric ratios of the angle A. Also find the six ratios of the angle C

**Solution : **

Given that 15 sin A = 12, so sin A = 12 / 15

Therefore, opposite side = 12 and hypotenuse = 15

Let us consider the triangle ABC where right angled at B, with BC = 12 and AC = 15.

By Pythagorean theorem,

AC² = AB² + BC²

15² = AB² + 12²

AB² = 15² - 12²

AB² = 225 - 144

AB² = 81

AB² = 9²

AB = 9

Now, we can use the three sides to find the five trigonometric ratios of angle A and six trigonometric ratios of angle C.

Therefore,

**Problem 4 :**

In the right triangle PQR given below, find the value of sinθ and cosθ. Using them, find the value of tanθ and cotθ

**Solution :**

From the figure given above,

opposite side = 5

adjacent side = 12

hypotenuse = 13

Therefore,

sinθ = PQ/RQ = 5/13

cosθ = PR/RQ = 12/13

tanθ = sinθ / cosθ = (5/13) ÷ (12/13)

tanθ = (5/13) x (13/12)

**tanθ = 5/12**

cotθ = cosθ / sinθ = (12/13) ÷ (5/13)

cotθ = (12/13) x (13/5)

**cotθ = 12/5**

**Problem 5 :**

From the figure given below, find the value of sinθ and cosθ. Using them, find the value of tanθ and cotθ

**Solution : **

From the figure given above, AC = 24 and BC = 7.

By Pythagorean theorem,

AB² = BC² + CA²

AB² = 7² + 24²

AB² = 49 + 576

AB² = 625

AB² = 25²

AB = 25

Now, we can use the three sides to find the six trigonometric ratios of angle θ.

Therefore,

opposite side = 7

adjacent side = 24

hypotenuse = 25

Therefore,

sinθ = BC/AB = 7/25

cosθ = AC/AB = 24/25

tanθ = sinθ / cosθ = (7/25) ÷ (24/25)

tanθ = (7/25) x (25/24)

**tanθ = 7/24**

sinθ = BC/AB = 7/25

cosθ = AC/AB = 24/25

cotθ = cosθ / sinθ = (24/25) ÷ (7/25)

cotθ = (24/25) x (25/7)

**cotθ = 24/7**

After having gone through the stuff given above, we hope that the students would have understood "Trigonometric ratios worksheet"

If you want to know more "Trigonometric ratios worksheet", please click here

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**