Question

Consider the non-right triangle below.Suppose that m∠CAB=62∘, and that x=35 cm and y=17 cm. What is the area of this triangle? cm^2

Answer 1

Based on the given parameters, the area of the triangle is approximately 262.67
`cm^2`.

How to find the area of a non-right triangle

To find the area of a non-right triangle, use the formula for the area of a triangle:

Area = (1/2) * base * height

In this case, side AB represents the base and side AC represents the height.

Given that x = 35 cm and y = 17 cm,

To find the area, calculate the height of the triangle, which is the perpendicular distance from point A to side BC. We can use trigonometry to find this height.

Using the given information, we have:

m∠CAB = 62°

Side AB = y = 17 cm

Side AC = x = 35 cm

Since angle CAB is 62°, angle BCA is 180° - 62° = 118°.

Now, use the sine function to find the height:

sin(118°) = height / x

height = x * sin(118°)

Substitute the values:

height = 35 cm * sin(118°)

Using a calculator, we find that sin(118°) ≈ 0.8829.

height ≈ 35 cm * 0.8829 ≈ 30.903 cm

Now, calculate the area:

Area = (1/2) * base * height

Area = (1/2) * y * height

Area = (1/2) * 17 cm * 30.903 cm

Calculating, we find:

Area ≈ 262.67
`cm^2`

Therefore, the area of the triangle is approximately 262.67
`cm^2`.

Answer 2

Given that:

x=35 cm and y=17 cm

and angle CAB= 62 degree

`\begin{gathered} A=(1)/(2)* x* y*\sin (\angle CAB) \\ A=(1)/(2)(35)(17)\sin (62) \\ A=297.5*\sin (62) \\ A=262.67cm^2 \end{gathered}`