What is the area of a triangle when its longest side is 162cm with angles of 37.25 degrees and 48.4 degrees?

Answer 1

The third angle of the triangle is 180° - (37.25° + 48.4°) = 94.35°

→ The longest side is opposite the third angle.

Using this as the bas of the triangle, the height of the triangle can be found using the Sine ratio on one of the other angles, eg the 37.25° angle:

height = hypotenuse × sin 37.25°

where the hypotenuse is the side opposite the other angle (of 48.4°)

Using the sine rule, this length can be found:

hypotenuse/sin 48.4° = 162cm/sin 94.35°

→ hypotenuse = 162 cm × sin 48.4°/sin 94.35°

→ height = 162 cm × sin 37.25° × sin 48.4°/sin 94.35°

→ area = ½ × base × height

= ½ × 162 cm × 162 cm × (sin 37.25° × sin 48.4°)/sin 94.35°

= ½ × (162 cm)² × (sin 37.25° × sin 48.4°)/sin 94.35°

At this point you can see that the area of the triangle is ½ × given_length² × product of sine of other angles / sine of angle opposite given side

area ≈ 5957 cm²

Answer 2

It is approx 5957 square centimetres.