Question

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.

What is the approximate area of the triangle? Round to the nearest tenth.

Area of a triangle = bh

68.7 cm2
161.7 cm2
381.3 cm2
450.0 cm2

Answer 1

Your answer is the second one 161.7cm2

Answer 2

Area of a triangle =
`(1)/(2) base*height`

In a right angle triangle the two legs are the base and height of the triangle.

One angle of the triangle is 23 degree and one adjacent leg is 27.6 cm.Let the other leg opposite to 23 degree angle by x.Sine of an angle is ratio of opposite and hypotenuse. Hypotenuse is given as 30 cm.

`Sin 23=(x)/(30)`

x= 30 sin23.

x=11.72cm.

The legs of the triangle are 11.72 cm and 27.6 cm.

Area of triangle =
`(1)/(2) x11.72 x27.6 =161.7cm^(2).`