Calculating a length

The three trigonometric ratios can be used to calculate the length of a side in a right-angled triangle.

Example

Calculate the length AB. Give the answer to one decimal place.

Right angle triangle (ABC) with sides a, h and o. 32degrees angle

Label the sides of the triangle o, a and h.

Next choose the correct ratio from s^o_h~c^a_h~t^o_a.

The length h is known and the length o must be calculated.

Use \sin{x} = \frac{o}{h}

\sin{32} = \frac{AB}{8}

Make AB the subject by multiplying both sides by 8.

AB = 8 \times \sin{32}

AB = 4.2 cm

It may be necessary to rearrange the formula to calculate a length.

Question

Calculate the length YZ. Give the answer to one decimal place.

Triangle (XYZ)

Label the sides of the triangle o, a and h.

Next choose the correct ratio from s^o_h~c^a_h~t^o_a.

The length a is known and the length h must be calculated.

Use: \cos{x} = \frac{a}{h}

\cos{25} = \frac{5}{\text{YZ}}

Rearrange the equation to make YZ the subject.

Multiply both sides by YZ.

\text{YZ} \times \cos{25} = 5

Divide both sides by \cos{25}.

YZ = \frac{5}{\cos{25}}

YZ = 5.0 cm