Question

Find the area of a right triangle whose hypotenuse is 10 cm and one of the acute angle is 24°24′

Answer 1

In the ΔABC,

sin 24°24′ = `"AB"/"AC"`

0.4131 = `"AB"/10`

∴ AB = 4.131 cm

In the ΔABC,

cos 24°24′ = `"BC"/"AC"`

0.9107 = `"BC"/10`

∴ BC = 9.107 cm

Area of the right angle = `1/2 xx "BC" xx "AB"`

= `1/2 xx 9.107 xx 4.131`

= `37.62/2`

Area of the triangle = 18.81 cm²