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Finding a missing side using trig (side on top of the fraction)

Updated on August 6, 2010

Trigonometry can be used to work out unknown sides and angles in right angled triangles. In this first article on trigonometry here on Hubpages, I will show you how to work out a missing side length using trigonometry. The missing side that will be finding will be the one where the side is on top of the trigonometric formula.

Before you start,  remember the 3 formulas that you use for trigonometry in right angled triangles are:

Sin Ѳ = 0/H

Cos Ѳ = A/H

Tan Ѳ = O/A

(Ѳ is the angle, H is the hypotenuse (longest side), O is the side opposite the angle, and A is the adjacent side).

Question 1

Work out the side length marked x using trigonometry.

To begin with label up your triangle. Make sure this is done correctly otherwise you will get the next bit wrong. Start by labelling the longest side H (92mm) and the side opposite the angle you are given O (this is x).

One this is done, you now need to choose the correct trigonometric formula. Since you have the hypotenuse and you want to find the opposite side, then it must be the formula with H and O.

Therefore, the formula that you need to use to solve this trigonometric problem is Sin Ѳ = 0/H

Sin Ѳ = 0/H

Sin 29 = x/92

x is on the numerator of the fraction, and is being divided by 92. So if you multiply both sides of the formula by 92 you will be given the value of x.

92 × sin29 = 44.6mm to 3 significant figures.

Question 2

Work out the side length marked x using trigonometry.

To begin with label up your triangle. Make sure this is done correctly otherwise you will get the next bit wrong. Start by labelling the longest side H (98mm) and the side opposite the angle you are given O. That leaves the third side which will be A (x)

One this is done, you now need to choose the correct trigonometric formula. Since you have the hypotenuse and you want to find the adjacent side, then it must be the formula with H and A.

Therefore, the formula that you need to use to solve this trigonometric problem is Sin Ѳ = 0/H

Cos Ѳ = A/H

Cos 24 = x/98

x is on the numerator of the fraction, and is being divided by 98. So if you multiply both sides of the formula by 98 you will be given the value of x.

98 × cos24 = 89.5 mm to 3 significant figures.

For some more trigonometric questions on working out the missing side length on top of the fraction then click here.

For some real life worked examples on trigonometry then click here.

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