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:
[tex]\text{Area}=\frac{1}{2}\ast b\ast h[/tex]
Where h is the height which was not given.
To find the height, apply trigonometric ratio formula for sine:
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Where:
Hypotenuse = 4 cm
Opposite side is the side opposite the given angle(θ) which is the height
θ = 37 degrees
thus, we have:
[tex]\begin{gathered} \sin 37=\frac{h}{4} \\ \\ \text{Multiply both sides by 4:} \\ 4(\sin 37)=\frac{h}{4}\ast4 \\ \\ 4(\sin 37)=h \\ \\ 4(0.602)=h \\ \\ 2.4=h \\ \\ h=2.4\operatorname{cm} \end{gathered}[/tex]
The height of the traingle is 2.4 cm.
To find the area of the traingle, we have:
[tex]\begin{gathered} \text{Area=}\frac{1}{2}\ast b\ast h \\ \\ \text{Area}=\frac{1}{2}\ast5\ast2.4 \\ \\ \text{Area}=\frac{1}{2}\ast12 \\ \\ ^{} \\ \text{ Area = 6 cm}^2 \end{gathered}[/tex]
Therefore, the area of the triangle is 6 square centimeters
ANSWER:
6 cm²
