GCSE(H),

The area of a right angled triangle is A = `frac(1)(2)`*bh*, where *b* is the base length and *h* is the vertical height.

For the triangle ABC, the area of the triangle is `frac(1)(2)`*bh*.

Using the trigonometrical ratios, the vertical height is *h* = *a* x sin *C*.

Substituting into the formula for *h* in the area of a right angled triangle:

A = `frac(1)(2)`*b* x *a* x sin *C*

= `frac(1)(2)`*ab* sin *C*

1. What is the area of the triangle, below? Give your answer correct to 2 decimal places.

Answer: 123.32 cm^{2}

Area of any triangle = `frac(1)(2)ab sin C`

`A = frac(1)(2) xx 14 xx 19 xx sin 68`

`A = 123.3155`, or 123.32 (2dp)

2. The area of the triangle below is 100 cm^{2}. What is the size of the angle *x*? Give your
answer correct to the nearest degree.

Answer: 34º

Area of any triangle = `frac(1)(2)ab sin C`

`100 = frac(1)(2) xx 18 xx 20 xx sin *x*`

`100 = 180 sin x`

`0.5556 = sin x`

`sin^-1^ 0.5556 = x`

`x = 33.749`, or 34º (nearest degree)

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