Question

a right triangle has one angle that measures 23 degress.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 =1/2bh

Answer 1

Sent a pic of the solution (s).

Answer 2

Area of the triangle will be 162.3 cm²

Explanation:

From the figure attached,

In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm

Now we have to calculate the area of the given right angle triangle.

Since area of a right angle triangle is represented by

Area =
`(1)/(2)* b* h`

Where b = adjacent side

h = opposite side

To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.

AC² = AB² + BC²

AB² = AC² - BC²

AB² = (30)² - (27.6)²

= 900 - 761.76

= 138.24

AB = √138.24

= 11.76

Area of the triangle =
`(1)/(2)(AB)(BC)`

=
`(1)/(2)(11.76)(27.6)`

= 162.28 cm² ≈ 162.3 cm²