# SOHCAHTOA WORKSHEET

## About "SOHCAHTOA Worksheet"

SOHCAHTOA Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on six trigonometric ratios sin, cosine, tangent, csc, sec and co-tangent. To understand the shortcut, first we have to divide SOHCAHTOA in to three parts as given below. What do SOH, CAH and TOA stand for ?

Here is the answer   From the above figures, we can derive formulas for the three trigonometric ratios sin, cos and tan as given below.   ## SOHCAHTOA Worksheet - Problems

1. In the right triangle PQR given below, find the six trigonometric ratios of the angle θ. 2.  From the figure 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.  ## SOHCAHTOA Worksheet - Solution

Problem 1 :

In the right triangle PQR 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, After having gone through the stuff given above, we hope that the students would have understood "SOHCAHTOA"

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