Question

Find the area and round all answers to the nearest hundredths.

Answer 1

Given:

Base, b = 5 cm

One side = 4 cm

Angle = 37 degrees

Let's find the area of the triangle.

To find the area of the triangle, apply the formula:

`\text{Area}=(1)/(2)\ast b\ast h`

Where h is the height which was not given.

To find the height, apply trigonometric ratio formula for sine:

`\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}`

Where:

Hypotenuse = 4 cm

Opposite side is the side opposite the given angle(θ) which is the height

θ = 37 degrees

thus, we have:

The height of the traingle is 2.4 cm.

To find the area of the traingle, we have:

`\begin{gathered} \text{Area=}(1)/(2)\ast b\ast h \\ \\ \text{Area}=(1)/(2)\ast5\ast2.4 \\ \\ \text{Area}=(1)/(2)\ast12 \\ \\ ^{} \\ \text{ Area = 6 cm}^2 \end{gathered}`

Therefore, the area of the triangle is 6 square centimeters

ANSWER:

6 cm²