Question

What is the area of ΔABC given a = 11 inches, b = 22 inches, and m∠C = 27°? 35.349 in.2 54.933 in.2 107.812 in.2 115.721 in.2

Answer 1

Explanationt

Finding the area of a triangle - when the height is not give,

The area of any triangle is given by one half the product of the lengths of two sides mes the sine of their included angle.

Area =
`(1)/(2)` × 11 × 22 × sin 27°

Area =
`(1)/(2)` × 11 × 22 × .454

Area = 121 × .454

Area = 54.933 in²

Answer 2

We can find the area using the following formula:

`\begin{gathered} A=(1)/(2)a\cdot b\cdot\sin (C) \\ _{\text{ }}where\colon \\ a=11 \\ b=22 \\ m\angle C=27 \\ so\colon \\ A=(1)/(2)\cdot11\cdot22\cdot\sin (27) \\ A=54.933_{\text{ }}in^2 \end{gathered}`

Answer:

54.933 in²